Worked solution P24-Easy-1. The population is the complete group addressed by the question; the sample is the observed subset; the parameter is the population summary; the statistic is the corresponding sample summary. If 84 of 120 sampled units have a characteristic, the statistic is $\widehat{p}=84/120=0.700$. The unknown population proportion is $p$. Interpretation: The value 0.700 describes the sample and estimates p only to the extent supported by the selection design. Validity: The observational unit, variable, target population, and sampling frame must be stated separately. Error to reject: Calling 0.700 a parameter reverses the distinction between observed sample evidence and an unknown population feature.

Worked solution P24-Easy-2. The population is the complete group addressed by the question; the sample is the observed subset; the parameter is the population summary; the statistic is the corresponding sample summary. If 84 of 120 sampled units have a characteristic, the statistic is $\widehat{p}=84/120=0.700$. The unknown population proportion is $p$. Interpretation: The value 0.700 describes the sample and estimates p only to the extent supported by the selection design. Validity: The observational unit, variable, target population, and sampling frame must be stated separately. Error to reject: Calling 0.700 a parameter reverses the distinction between observed sample evidence and an unknown population feature.

Worked solution P24-Easy-3. The population is the complete group addressed by the question; the sample is the observed subset; the parameter is the population summary; the statistic is the corresponding sample summary. If 84 of 120 sampled units have a characteristic, the statistic is $\widehat{p}=84/120=0.700$. The unknown population proportion is $p$. Interpretation: The value 0.700 describes the sample and estimates p only to the extent supported by the selection design. Validity: The observational unit, variable, target population, and sampling frame must be stated separately. Error to reject: Calling 0.700 a parameter reverses the distinction between observed sample evidence and an unknown population feature.

Worked solution P24-Easy-4. The population is the complete group addressed by the question; the sample is the observed subset; the parameter is the population summary; the statistic is the corresponding sample summary. If 84 of 120 sampled units have a characteristic, the statistic is $\widehat{p}=84/120=0.700$. The unknown population proportion is $p$. Interpretation: The value 0.700 describes the sample and estimates p only to the extent supported by the selection design. Validity: The observational unit, variable, target population, and sampling frame must be stated separately. Error to reject: Calling 0.700 a parameter reverses the distinction between observed sample evidence and an unknown population feature.

Worked solution P24-Easy-5. The population is the complete group addressed by the question; the sample is the observed subset; the parameter is the population summary; the statistic is the corresponding sample summary. If 84 of 120 sampled units have a characteristic, the statistic is $\widehat{p}=84/120=0.700$. The unknown population proportion is $p$. Interpretation: The value 0.700 describes the sample and estimates p only to the extent supported by the selection design. Validity: The observational unit, variable, target population, and sampling frame must be stated separately. Error to reject: Calling 0.700 a parameter reverses the distinction between observed sample evidence and an unknown population feature.

Worked solution P24-Easy-6. The population is the complete group addressed by the question; the sample is the observed subset; the parameter is the population summary; the statistic is the corresponding sample summary. If 84 of 120 sampled units have a characteristic, the statistic is $\widehat{p}=84/120=0.700$. The unknown population proportion is $p$. Interpretation: The value 0.700 describes the sample and estimates p only to the extent supported by the selection design. Validity: The observational unit, variable, target population, and sampling frame must be stated separately. Error to reject: Calling 0.700 a parameter reverses the distinction between observed sample evidence and an unknown population feature.

Worked solution P24-Easy-7. The population is the complete group addressed by the question; the sample is the observed subset; the parameter is the population summary; the statistic is the corresponding sample summary. If 84 of 120 sampled units have a characteristic, the statistic is $\widehat{p}=84/120=0.700$. The unknown population proportion is $p$. Interpretation: The value 0.700 describes the sample and estimates p only to the extent supported by the selection design. Validity: The observational unit, variable, target population, and sampling frame must be stated separately. Error to reject: Calling 0.700 a parameter reverses the distinction between observed sample evidence and an unknown population feature.

Worked solution P24-Easy-8. The population is the complete group addressed by the question; the sample is the observed subset; the parameter is the population summary; the statistic is the corresponding sample summary. If 84 of 120 sampled units have a characteristic, the statistic is $\widehat{p}=84/120=0.700$. The unknown population proportion is $p$. Interpretation: The value 0.700 describes the sample and estimates p only to the extent supported by the selection design. Validity: The observational unit, variable, target population, and sampling frame must be stated separately. Error to reject: Calling 0.700 a parameter reverses the distinction between observed sample evidence and an unknown population feature.

Worked solution P24-Easy-9. The population is the complete group addressed by the question; the sample is the observed subset; the parameter is the population summary; the statistic is the corresponding sample summary. If 84 of 120 sampled units have a characteristic, the statistic is $\widehat{p}=84/120=0.700$. The unknown population proportion is $p$. Interpretation: The value 0.700 describes the sample and estimates p only to the extent supported by the selection design. Validity: The observational unit, variable, target population, and sampling frame must be stated separately. Error to reject: Calling 0.700 a parameter reverses the distinction between observed sample evidence and an unknown population feature.

Worked solution P24-Easy-10. The population is the complete group addressed by the question; the sample is the observed subset; the parameter is the population summary; the statistic is the corresponding sample summary. If 84 of 120 sampled units have a characteristic, the statistic is $\widehat{p}=84/120=0.700$. The unknown population proportion is $p$. Interpretation: The value 0.700 describes the sample and estimates p only to the extent supported by the selection design. Validity: The observational unit, variable, target population, and sampling frame must be stated separately. Error to reject: Calling 0.700 a parameter reverses the distinction between observed sample evidence and an unknown population feature.

Worked solution P24-Easy-11. The population is the complete group addressed by the question; the sample is the observed subset; the parameter is the population summary; the statistic is the corresponding sample summary. If 84 of 120 sampled units have a characteristic, the statistic is $\widehat{p}=84/120=0.700$. The unknown population proportion is $p$. Interpretation: The value 0.700 describes the sample and estimates p only to the extent supported by the selection design. Validity: The observational unit, variable, target population, and sampling frame must be stated separately. Error to reject: Calling 0.700 a parameter reverses the distinction between observed sample evidence and an unknown population feature.

Worked solution P24-Easy-12. The population is the complete group addressed by the question; the sample is the observed subset; the parameter is the population summary; the statistic is the corresponding sample summary. If 84 of 120 sampled units have a characteristic, the statistic is $\widehat{p}=84/120=0.700$. The unknown population proportion is $p$. Interpretation: The value 0.700 describes the sample and estimates p only to the extent supported by the selection design. Validity: The observational unit, variable, target population, and sampling frame must be stated separately. Error to reject: Calling 0.700 a parameter reverses the distinction between observed sample evidence and an unknown population feature.

Worked solution P24-Easy-13. The population is the complete group addressed by the question; the sample is the observed subset; the parameter is the population summary; the statistic is the corresponding sample summary. If 84 of 120 sampled units have a characteristic, the statistic is $\widehat{p}=84/120=0.700$. The unknown population proportion is $p$. Interpretation: The value 0.700 describes the sample and estimates p only to the extent supported by the selection design. Validity: The observational unit, variable, target population, and sampling frame must be stated separately. Error to reject: Calling 0.700 a parameter reverses the distinction between observed sample evidence and an unknown population feature.

Worked solution P24-Easy-14. The population is the complete group addressed by the question; the sample is the observed subset; the parameter is the population summary; the statistic is the corresponding sample summary. If 84 of 120 sampled units have a characteristic, the statistic is $\widehat{p}=84/120=0.700$. The unknown population proportion is $p$. Interpretation: The value 0.700 describes the sample and estimates p only to the extent supported by the selection design. Validity: The observational unit, variable, target population, and sampling frame must be stated separately. Error to reject: Calling 0.700 a parameter reverses the distinction between observed sample evidence and an unknown population feature.

Worked solution P24-Easy-15. The population is the complete group addressed by the question; the sample is the observed subset; the parameter is the population summary; the statistic is the corresponding sample summary. If 84 of 120 sampled units have a characteristic, the statistic is $\widehat{p}=84/120=0.700$. The unknown population proportion is $p$. Interpretation: The value 0.700 describes the sample and estimates p only to the extent supported by the selection design. Validity: The observational unit, variable, target population, and sampling frame must be stated separately. Error to reject: Calling 0.700 a parameter reverses the distinction between observed sample evidence and an unknown population feature.

Worked solution P24-Easy-16. The population is the complete group addressed by the question; the sample is the observed subset; the parameter is the population summary; the statistic is the corresponding sample summary. If 84 of 120 sampled units have a characteristic, the statistic is $\widehat{p}=84/120=0.700$. The unknown population proportion is $p$. Interpretation: The value 0.700 describes the sample and estimates p only to the extent supported by the selection design. Validity: The observational unit, variable, target population, and sampling frame must be stated separately. Error to reject: Calling 0.700 a parameter reverses the distinction between observed sample evidence and an unknown population feature.

Worked solution P24-Easy-17. The population is the complete group addressed by the question; the sample is the observed subset; the parameter is the population summary; the statistic is the corresponding sample summary. If 84 of 120 sampled units have a characteristic, the statistic is $\widehat{p}=84/120=0.700$. The unknown population proportion is $p$. Interpretation: The value 0.700 describes the sample and estimates p only to the extent supported by the selection design. Validity: The observational unit, variable, target population, and sampling frame must be stated separately. Error to reject: Calling 0.700 a parameter reverses the distinction between observed sample evidence and an unknown population feature.

Worked solution P24-Tough-1. The population is the complete group addressed by the question; the sample is the observed subset; the parameter is the population summary; the statistic is the corresponding sample summary. If 84 of 120 sampled units have a characteristic, the statistic is $\widehat{p}=84/120=0.700$. The unknown population proportion is $p$. Interpretation: The value 0.700 describes the sample and estimates p only to the extent supported by the selection design. Validity: The observational unit, variable, target population, and sampling frame must be stated separately. Error to reject: Calling 0.700 a parameter reverses the distinction between observed sample evidence and an unknown population feature.

Worked solution P24-Tough-2. The population is the complete group addressed by the question; the sample is the observed subset; the parameter is the population summary; the statistic is the corresponding sample summary. If 84 of 120 sampled units have a characteristic, the statistic is $\widehat{p}=84/120=0.700$. The unknown population proportion is $p$. Interpretation: The value 0.700 describes the sample and estimates p only to the extent supported by the selection design. Validity: The observational unit, variable, target population, and sampling frame must be stated separately. Error to reject: Calling 0.700 a parameter reverses the distinction between observed sample evidence and an unknown population feature.

Worked solution P24-Tough-3. The population is the complete group addressed by the question; the sample is the observed subset; the parameter is the population summary; the statistic is the corresponding sample summary. If 84 of 120 sampled units have a characteristic, the statistic is $\widehat{p}=84/120=0.700$. The unknown population proportion is $p$. Interpretation: The value 0.700 describes the sample and estimates p only to the extent supported by the selection design. Validity: The observational unit, variable, target population, and sampling frame must be stated separately. Error to reject: Calling 0.700 a parameter reverses the distinction between observed sample evidence and an unknown population feature.

Worked solution P24-Tough-4. The population is the complete group addressed by the question; the sample is the observed subset; the parameter is the population summary; the statistic is the corresponding sample summary. If 84 of 120 sampled units have a characteristic, the statistic is $\widehat{p}=84/120=0.700$. The unknown population proportion is $p$. Interpretation: The value 0.700 describes the sample and estimates p only to the extent supported by the selection design. Validity: The observational unit, variable, target population, and sampling frame must be stated separately. Error to reject: Calling 0.700 a parameter reverses the distinction between observed sample evidence and an unknown population feature.

Worked solution P24-Tough-5. The population is the complete group addressed by the question; the sample is the observed subset; the parameter is the population summary; the statistic is the corresponding sample summary. If 84 of 120 sampled units have a characteristic, the statistic is $\widehat{p}=84/120=0.700$. The unknown population proportion is $p$. Interpretation: The value 0.700 describes the sample and estimates p only to the extent supported by the selection design. Validity: The observational unit, variable, target population, and sampling frame must be stated separately. Error to reject: Calling 0.700 a parameter reverses the distinction between observed sample evidence and an unknown population feature.

Worked solution P24-Tough-6. The population is the complete group addressed by the question; the sample is the observed subset; the parameter is the population summary; the statistic is the corresponding sample summary. If 84 of 120 sampled units have a characteristic, the statistic is $\widehat{p}=84/120=0.700$. The unknown population proportion is $p$. Interpretation: The value 0.700 describes the sample and estimates p only to the extent supported by the selection design. Validity: The observational unit, variable, target population, and sampling frame must be stated separately. Error to reject: Calling 0.700 a parameter reverses the distinction between observed sample evidence and an unknown population feature.

Worked solution P24-Tough-7. The population is the complete group addressed by the question; the sample is the observed subset; the parameter is the population summary; the statistic is the corresponding sample summary. If 84 of 120 sampled units have a characteristic, the statistic is $\widehat{p}=84/120=0.700$. The unknown population proportion is $p$. Interpretation: The value 0.700 describes the sample and estimates p only to the extent supported by the selection design. Validity: The observational unit, variable, target population, and sampling frame must be stated separately. Error to reject: Calling 0.700 a parameter reverses the distinction between observed sample evidence and an unknown population feature.

Worked solution P24-Tough-8. The population is the complete group addressed by the question; the sample is the observed subset; the parameter is the population summary; the statistic is the corresponding sample summary. If 84 of 120 sampled units have a characteristic, the statistic is $\widehat{p}=84/120=0.700$. The unknown population proportion is $p$. Interpretation: The value 0.700 describes the sample and estimates p only to the extent supported by the selection design. Validity: The observational unit, variable, target population, and sampling frame must be stated separately. Error to reject: Calling 0.700 a parameter reverses the distinction between observed sample evidence and an unknown population feature.

Worked solution P24-Tough-9. The population is the complete group addressed by the question; the sample is the observed subset; the parameter is the population summary; the statistic is the corresponding sample summary. If 84 of 120 sampled units have a characteristic, the statistic is $\widehat{p}=84/120=0.700$. The unknown population proportion is $p$. Interpretation: The value 0.700 describes the sample and estimates p only to the extent supported by the selection design. Validity: The observational unit, variable, target population, and sampling frame must be stated separately. Error to reject: Calling 0.700 a parameter reverses the distinction between observed sample evidence and an unknown population feature.

Worked solution P24-Tough-10. The population is the complete group addressed by the question; the sample is the observed subset; the parameter is the population summary; the statistic is the corresponding sample summary. If 84 of 120 sampled units have a characteristic, the statistic is $\widehat{p}=84/120=0.700$. The unknown population proportion is $p$. Interpretation: The value 0.700 describes the sample and estimates p only to the extent supported by the selection design. Validity: The observational unit, variable, target population, and sampling frame must be stated separately. Error to reject: Calling 0.700 a parameter reverses the distinction between observed sample evidence and an unknown population feature.

Worked solution P24-Tough-11. The population is the complete group addressed by the question; the sample is the observed subset; the parameter is the population summary; the statistic is the corresponding sample summary. If 84 of 120 sampled units have a characteristic, the statistic is $\widehat{p}=84/120=0.700$. The unknown population proportion is $p$. Interpretation: The value 0.700 describes the sample and estimates p only to the extent supported by the selection design. Validity: The observational unit, variable, target population, and sampling frame must be stated separately. Error to reject: Calling 0.700 a parameter reverses the distinction between observed sample evidence and an unknown population feature.

Worked solution P24-Tough-12. The population is the complete group addressed by the question; the sample is the observed subset; the parameter is the population summary; the statistic is the corresponding sample summary. If 84 of 120 sampled units have a characteristic, the statistic is $\widehat{p}=84/120=0.700$. The unknown population proportion is $p$. Interpretation: The value 0.700 describes the sample and estimates p only to the extent supported by the selection design. Validity: The observational unit, variable, target population, and sampling frame must be stated separately. Error to reject: Calling 0.700 a parameter reverses the distinction between observed sample evidence and an unknown population feature.

Worked solution P24-Tough-13. The population is the complete group addressed by the question; the sample is the observed subset; the parameter is the population summary; the statistic is the corresponding sample summary. If 84 of 120 sampled units have a characteristic, the statistic is $\widehat{p}=84/120=0.700$. The unknown population proportion is $p$. Interpretation: The value 0.700 describes the sample and estimates p only to the extent supported by the selection design. Validity: The observational unit, variable, target population, and sampling frame must be stated separately. Error to reject: Calling 0.700 a parameter reverses the distinction between observed sample evidence and an unknown population feature.

Worked solution P24-Tough-14. The population is the complete group addressed by the question; the sample is the observed subset; the parameter is the population summary; the statistic is the corresponding sample summary. If 84 of 120 sampled units have a characteristic, the statistic is $\widehat{p}=84/120=0.700$. The unknown population proportion is $p$. Interpretation: The value 0.700 describes the sample and estimates p only to the extent supported by the selection design. Validity: The observational unit, variable, target population, and sampling frame must be stated separately. Error to reject: Calling 0.700 a parameter reverses the distinction between observed sample evidence and an unknown population feature.

Worked solution P24-Tough-15. The population is the complete group addressed by the question; the sample is the observed subset; the parameter is the population summary; the statistic is the corresponding sample summary. If 84 of 120 sampled units have a characteristic, the statistic is $\widehat{p}=84/120=0.700$. The unknown population proportion is $p$. Interpretation: The value 0.700 describes the sample and estimates p only to the extent supported by the selection design. Validity: The observational unit, variable, target population, and sampling frame must be stated separately. Error to reject: Calling 0.700 a parameter reverses the distinction between observed sample evidence and an unknown population feature.

Worked solution P24-Tough-16. The population is the complete group addressed by the question; the sample is the observed subset; the parameter is the population summary; the statistic is the corresponding sample summary. If 84 of 120 sampled units have a characteristic, the statistic is $\widehat{p}=84/120=0.700$. The unknown population proportion is $p$. Interpretation: The value 0.700 describes the sample and estimates p only to the extent supported by the selection design. Validity: The observational unit, variable, target population, and sampling frame must be stated separately. Error to reject: Calling 0.700 a parameter reverses the distinction between observed sample evidence and an unknown population feature.

Worked solution P24-Tough-17. The population is the complete group addressed by the question; the sample is the observed subset; the parameter is the population summary; the statistic is the corresponding sample summary. If 84 of 120 sampled units have a characteristic, the statistic is $\widehat{p}=84/120=0.700$. The unknown population proportion is $p$. Interpretation: The value 0.700 describes the sample and estimates p only to the extent supported by the selection design. Validity: The observational unit, variable, target population, and sampling frame must be stated separately. Error to reject: Calling 0.700 a parameter reverses the distinction between observed sample evidence and an unknown population feature.

Worked solution P24-Toughest-1. The population is the complete group addressed by the question; the sample is the observed subset; the parameter is the population summary; the statistic is the corresponding sample summary. If 84 of 120 sampled units have a characteristic, the statistic is $\widehat{p}=84/120=0.700$. The unknown population proportion is $p$. Interpretation: The value 0.700 describes the sample and estimates p only to the extent supported by the selection design. Validity: The observational unit, variable, target population, and sampling frame must be stated separately. Error to reject: Calling 0.700 a parameter reverses the distinction between observed sample evidence and an unknown population feature.

Worked solution P24-Toughest-2. The population is the complete group addressed by the question; the sample is the observed subset; the parameter is the population summary; the statistic is the corresponding sample summary. If 84 of 120 sampled units have a characteristic, the statistic is $\widehat{p}=84/120=0.700$. The unknown population proportion is $p$. Interpretation: The value 0.700 describes the sample and estimates p only to the extent supported by the selection design. Validity: The observational unit, variable, target population, and sampling frame must be stated separately. Error to reject: Calling 0.700 a parameter reverses the distinction between observed sample evidence and an unknown population feature.

Worked solution P24-Toughest-3. The population is the complete group addressed by the question; the sample is the observed subset; the parameter is the population summary; the statistic is the corresponding sample summary. If 84 of 120 sampled units have a characteristic, the statistic is $\widehat{p}=84/120=0.700$. The unknown population proportion is $p$. Interpretation: The value 0.700 describes the sample and estimates p only to the extent supported by the selection design. Validity: The observational unit, variable, target population, and sampling frame must be stated separately. Error to reject: Calling 0.700 a parameter reverses the distinction between observed sample evidence and an unknown population feature.

Worked solution P24-Toughest-4. The population is the complete group addressed by the question; the sample is the observed subset; the parameter is the population summary; the statistic is the corresponding sample summary. If 84 of 120 sampled units have a characteristic, the statistic is $\widehat{p}=84/120=0.700$. The unknown population proportion is $p$. Interpretation: The value 0.700 describes the sample and estimates p only to the extent supported by the selection design. Validity: The observational unit, variable, target population, and sampling frame must be stated separately. Error to reject: Calling 0.700 a parameter reverses the distinction between observed sample evidence and an unknown population feature.

Worked solution P24-Toughest-5. The population is the complete group addressed by the question; the sample is the observed subset; the parameter is the population summary; the statistic is the corresponding sample summary. If 84 of 120 sampled units have a characteristic, the statistic is $\widehat{p}=84/120=0.700$. The unknown population proportion is $p$. Interpretation: The value 0.700 describes the sample and estimates p only to the extent supported by the selection design. Validity: The observational unit, variable, target population, and sampling frame must be stated separately. Error to reject: Calling 0.700 a parameter reverses the distinction between observed sample evidence and an unknown population feature.

Worked solution P24-Toughest-6. The population is the complete group addressed by the question; the sample is the observed subset; the parameter is the population summary; the statistic is the corresponding sample summary. If 84 of 120 sampled units have a characteristic, the statistic is $\widehat{p}=84/120=0.700$. The unknown population proportion is $p$. Interpretation: The value 0.700 describes the sample and estimates p only to the extent supported by the selection design. Validity: The observational unit, variable, target population, and sampling frame must be stated separately. Error to reject: Calling 0.700 a parameter reverses the distinction between observed sample evidence and an unknown population feature.

Worked solution P24-Toughest-7. The population is the complete group addressed by the question; the sample is the observed subset; the parameter is the population summary; the statistic is the corresponding sample summary. If 84 of 120 sampled units have a characteristic, the statistic is $\widehat{p}=84/120=0.700$. The unknown population proportion is $p$. Interpretation: The value 0.700 describes the sample and estimates p only to the extent supported by the selection design. Validity: The observational unit, variable, target population, and sampling frame must be stated separately. Error to reject: Calling 0.700 a parameter reverses the distinction between observed sample evidence and an unknown population feature.

Worked solution P24-Toughest-8. The population is the complete group addressed by the question; the sample is the observed subset; the parameter is the population summary; the statistic is the corresponding sample summary. If 84 of 120 sampled units have a characteristic, the statistic is $\widehat{p}=84/120=0.700$. The unknown population proportion is $p$. Interpretation: The value 0.700 describes the sample and estimates p only to the extent supported by the selection design. Validity: The observational unit, variable, target population, and sampling frame must be stated separately. Error to reject: Calling 0.700 a parameter reverses the distinction between observed sample evidence and an unknown population feature.

Worked solution P24-Toughest-9. The population is the complete group addressed by the question; the sample is the observed subset; the parameter is the population summary; the statistic is the corresponding sample summary. If 84 of 120 sampled units have a characteristic, the statistic is $\widehat{p}=84/120=0.700$. The unknown population proportion is $p$. Interpretation: The value 0.700 describes the sample and estimates p only to the extent supported by the selection design. Validity: The observational unit, variable, target population, and sampling frame must be stated separately. Error to reject: Calling 0.700 a parameter reverses the distinction between observed sample evidence and an unknown population feature.

Worked solution P24-Toughest-10. The population is the complete group addressed by the question; the sample is the observed subset; the parameter is the population summary; the statistic is the corresponding sample summary. If 84 of 120 sampled units have a characteristic, the statistic is $\widehat{p}=84/120=0.700$. The unknown population proportion is $p$. Interpretation: The value 0.700 describes the sample and estimates p only to the extent supported by the selection design. Validity: The observational unit, variable, target population, and sampling frame must be stated separately. Error to reject: Calling 0.700 a parameter reverses the distinction between observed sample evidence and an unknown population feature.

Worked solution P24-Toughest-11. The population is the complete group addressed by the question; the sample is the observed subset; the parameter is the population summary; the statistic is the corresponding sample summary. If 84 of 120 sampled units have a characteristic, the statistic is $\widehat{p}=84/120=0.700$. The unknown population proportion is $p$. Interpretation: The value 0.700 describes the sample and estimates p only to the extent supported by the selection design. Validity: The observational unit, variable, target population, and sampling frame must be stated separately. Error to reject: Calling 0.700 a parameter reverses the distinction between observed sample evidence and an unknown population feature.

Worked solution P24-Toughest-12. The population is the complete group addressed by the question; the sample is the observed subset; the parameter is the population summary; the statistic is the corresponding sample summary. If 84 of 120 sampled units have a characteristic, the statistic is $\widehat{p}=84/120=0.700$. The unknown population proportion is $p$. Interpretation: The value 0.700 describes the sample and estimates p only to the extent supported by the selection design. Validity: The observational unit, variable, target population, and sampling frame must be stated separately. Error to reject: Calling 0.700 a parameter reverses the distinction between observed sample evidence and an unknown population feature.

Worked solution P24-Toughest-13. The population is the complete group addressed by the question; the sample is the observed subset; the parameter is the population summary; the statistic is the corresponding sample summary. If 84 of 120 sampled units have a characteristic, the statistic is $\widehat{p}=84/120=0.700$. The unknown population proportion is $p$. Interpretation: The value 0.700 describes the sample and estimates p only to the extent supported by the selection design. Validity: The observational unit, variable, target population, and sampling frame must be stated separately. Error to reject: Calling 0.700 a parameter reverses the distinction between observed sample evidence and an unknown population feature.

Worked solution P24-Toughest-14. The population is the complete group addressed by the question; the sample is the observed subset; the parameter is the population summary; the statistic is the corresponding sample summary. If 84 of 120 sampled units have a characteristic, the statistic is $\widehat{p}=84/120=0.700$. The unknown population proportion is $p$. Interpretation: The value 0.700 describes the sample and estimates p only to the extent supported by the selection design. Validity: The observational unit, variable, target population, and sampling frame must be stated separately. Error to reject: Calling 0.700 a parameter reverses the distinction between observed sample evidence and an unknown population feature.

Worked solution P24-Toughest-15. The population is the complete group addressed by the question; the sample is the observed subset; the parameter is the population summary; the statistic is the corresponding sample summary. If 84 of 120 sampled units have a characteristic, the statistic is $\widehat{p}=84/120=0.700$. The unknown population proportion is $p$. Interpretation: The value 0.700 describes the sample and estimates p only to the extent supported by the selection design. Validity: The observational unit, variable, target population, and sampling frame must be stated separately. Error to reject: Calling 0.700 a parameter reverses the distinction between observed sample evidence and an unknown population feature.

Worked solution P24-Toughest-16. The population is the complete group addressed by the question; the sample is the observed subset; the parameter is the population summary; the statistic is the corresponding sample summary. If 84 of 120 sampled units have a characteristic, the statistic is $\widehat{p}=84/120=0.700$. The unknown population proportion is $p$. Interpretation: The value 0.700 describes the sample and estimates p only to the extent supported by the selection design. Validity: The observational unit, variable, target population, and sampling frame must be stated separately. Error to reject: Calling 0.700 a parameter reverses the distinction between observed sample evidence and an unknown population feature.

Worked solution P24-Toughest-17. The population is the complete group addressed by the question; the sample is the observed subset; the parameter is the population summary; the statistic is the corresponding sample summary. If 84 of 120 sampled units have a characteristic, the statistic is $\widehat{p}=84/120=0.700$. The unknown population proportion is $p$. Interpretation: The value 0.700 describes the sample and estimates p only to the extent supported by the selection design. Validity: The observational unit, variable, target population, and sampling frame must be stated separately. Error to reject: Calling 0.700 a parameter reverses the distinction between observed sample evidence and an unknown population feature.