Worked solution P61-Easy-1. Let p be the population proportion in context. Use $H_0:p=0.50$ and $H_a:p\>0.50$. The null contains equality because the reference distribution is computed under the specific value 0.50. Interpretation: Make the alpha comparison, state reject or fail to reject H0, and conclude in terms of evidence for the population claim. Validity: Choose direction from the research claim before seeing sample results and define p with population and success category. Error to reject: Do not write hypotheses with sample proportion hat p; observed statistics are evidence, not unknown claims.

Worked solution P61-Easy-2. Let p be the population proportion in context. Use $H_0:p=0.50$ and $H_a:p\<0.50$. The null contains equality because the reference distribution is computed under the specific value 0.50. Interpretation: Make the alpha comparison, state reject or fail to reject H0, and conclude in terms of evidence for the population claim. Validity: Choose direction from the research claim before seeing sample results and define p with population and success category. Error to reject: Do not write hypotheses with sample proportion hat p; observed statistics are evidence, not unknown claims.

Worked solution P61-Easy-3. Let p be the population proportion in context. Use $H_0:p=0.50$ and $H_a:p\ne 0.50$. The null contains equality because the reference distribution is computed under the specific value 0.50. Interpretation: Make the alpha comparison, state reject or fail to reject H0, and conclude in terms of evidence for the population claim. Validity: Choose direction from the research claim before seeing sample results and define p with population and success category. Error to reject: Do not write hypotheses with sample proportion hat p; observed statistics are evidence, not unknown claims.

Worked solution P61-Easy-4. Let p be the population proportion in context. Use $H_0:p=0.50$ and $H_a:p\>0.50$. The null contains equality because the reference distribution is computed under the specific value 0.50. Interpretation: Make the alpha comparison, state reject or fail to reject H0, and conclude in terms of evidence for the population claim. Validity: Choose direction from the research claim before seeing sample results and define p with population and success category. Error to reject: Do not write hypotheses with sample proportion hat p; observed statistics are evidence, not unknown claims.

Worked solution P61-Easy-5. Let p be the population proportion in context. Use $H_0:p=0.50$ and $H_a:p\<0.50$. The null contains equality because the reference distribution is computed under the specific value 0.50. Interpretation: Make the alpha comparison, state reject or fail to reject H0, and conclude in terms of evidence for the population claim. Validity: Choose direction from the research claim before seeing sample results and define p with population and success category. Error to reject: Do not write hypotheses with sample proportion hat p; observed statistics are evidence, not unknown claims.

Worked solution P61-Easy-6. Let p be the population proportion in context. Use $H_0:p=0.50$ and $H_a:p\ne 0.50$. The null contains equality because the reference distribution is computed under the specific value 0.50. Interpretation: Make the alpha comparison, state reject or fail to reject H0, and conclude in terms of evidence for the population claim. Validity: Choose direction from the research claim before seeing sample results and define p with population and success category. Error to reject: Do not write hypotheses with sample proportion hat p; observed statistics are evidence, not unknown claims.

Worked solution P61-Easy-7. Let p be the population proportion in context. Use $H_0:p=0.50$ and $H_a:p\>0.50$. The null contains equality because the reference distribution is computed under the specific value 0.50. Interpretation: Make the alpha comparison, state reject or fail to reject H0, and conclude in terms of evidence for the population claim. Validity: Choose direction from the research claim before seeing sample results and define p with population and success category. Error to reject: Do not write hypotheses with sample proportion hat p; observed statistics are evidence, not unknown claims.

Worked solution P61-Easy-8. Let p be the population proportion in context. Use $H_0:p=0.50$ and $H_a:p\<0.50$. The null contains equality because the reference distribution is computed under the specific value 0.50. Interpretation: Make the alpha comparison, state reject or fail to reject H0, and conclude in terms of evidence for the population claim. Validity: Choose direction from the research claim before seeing sample results and define p with population and success category. Error to reject: Do not write hypotheses with sample proportion hat p; observed statistics are evidence, not unknown claims.

Worked solution P61-Easy-9. Let p be the population proportion in context. Use $H_0:p=0.50$ and $H_a:p\ne 0.50$. The null contains equality because the reference distribution is computed under the specific value 0.50. Interpretation: Make the alpha comparison, state reject or fail to reject H0, and conclude in terms of evidence for the population claim. Validity: Choose direction from the research claim before seeing sample results and define p with population and success category. Error to reject: Do not write hypotheses with sample proportion hat p; observed statistics are evidence, not unknown claims.

Worked solution P61-Easy-10. Let p be the population proportion in context. Use $H_0:p=0.50$ and $H_a:p\>0.50$. The null contains equality because the reference distribution is computed under the specific value 0.50. Interpretation: Make the alpha comparison, state reject or fail to reject H0, and conclude in terms of evidence for the population claim. Validity: Choose direction from the research claim before seeing sample results and define p with population and success category. Error to reject: Do not write hypotheses with sample proportion hat p; observed statistics are evidence, not unknown claims.

Worked solution P61-Easy-11. Let p be the population proportion in context. Use $H_0:p=0.50$ and $H_a:p\<0.50$. The null contains equality because the reference distribution is computed under the specific value 0.50. Interpretation: Make the alpha comparison, state reject or fail to reject H0, and conclude in terms of evidence for the population claim. Validity: Choose direction from the research claim before seeing sample results and define p with population and success category. Error to reject: Do not write hypotheses with sample proportion hat p; observed statistics are evidence, not unknown claims.

Worked solution P61-Easy-12. Let p be the population proportion in context. Use $H_0:p=0.50$ and $H_a:p\ne 0.50$. The null contains equality because the reference distribution is computed under the specific value 0.50. Interpretation: Make the alpha comparison, state reject or fail to reject H0, and conclude in terms of evidence for the population claim. Validity: Choose direction from the research claim before seeing sample results and define p with population and success category. Error to reject: Do not write hypotheses with sample proportion hat p; observed statistics are evidence, not unknown claims.

Worked solution P61-Easy-13. Let p be the population proportion in context. Use $H_0:p=0.50$ and $H_a:p\>0.50$. The null contains equality because the reference distribution is computed under the specific value 0.50. Interpretation: Make the alpha comparison, state reject or fail to reject H0, and conclude in terms of evidence for the population claim. Validity: Choose direction from the research claim before seeing sample results and define p with population and success category. Error to reject: Do not write hypotheses with sample proportion hat p; observed statistics are evidence, not unknown claims.

Worked solution P61-Easy-14. Let p be the population proportion in context. Use $H_0:p=0.50$ and $H_a:p\<0.50$. The null contains equality because the reference distribution is computed under the specific value 0.50. Interpretation: Make the alpha comparison, state reject or fail to reject H0, and conclude in terms of evidence for the population claim. Validity: Choose direction from the research claim before seeing sample results and define p with population and success category. Error to reject: Do not write hypotheses with sample proportion hat p; observed statistics are evidence, not unknown claims.

Worked solution P61-Easy-15. Let p be the population proportion in context. Use $H_0:p=0.50$ and $H_a:p\ne 0.50$. The null contains equality because the reference distribution is computed under the specific value 0.50. Interpretation: Make the alpha comparison, state reject or fail to reject H0, and conclude in terms of evidence for the population claim. Validity: Choose direction from the research claim before seeing sample results and define p with population and success category. Error to reject: Do not write hypotheses with sample proportion hat p; observed statistics are evidence, not unknown claims.

Worked solution P61-Easy-16. Let p be the population proportion in context. Use $H_0:p=0.50$ and $H_a:p\>0.50$. The null contains equality because the reference distribution is computed under the specific value 0.50. Interpretation: Make the alpha comparison, state reject or fail to reject H0, and conclude in terms of evidence for the population claim. Validity: Choose direction from the research claim before seeing sample results and define p with population and success category. Error to reject: Do not write hypotheses with sample proportion hat p; observed statistics are evidence, not unknown claims.

Worked solution P61-Tough-1. Let p be the population proportion in context. Use $H_0:p=0.50$ and $H_a:p\>0.50$. The null contains equality because the reference distribution is computed under the specific value 0.50. Interpretation: Make the alpha comparison, state reject or fail to reject H0, and conclude in terms of evidence for the population claim. Validity: Choose direction from the research claim before seeing sample results and define p with population and success category. Error to reject: Do not write hypotheses with sample proportion hat p; observed statistics are evidence, not unknown claims.

Worked solution P61-Tough-2. Let p be the population proportion in context. Use $H_0:p=0.50$ and $H_a:p\<0.50$. The null contains equality because the reference distribution is computed under the specific value 0.50. Interpretation: Make the alpha comparison, state reject or fail to reject H0, and conclude in terms of evidence for the population claim. Validity: Choose direction from the research claim before seeing sample results and define p with population and success category. Error to reject: Do not write hypotheses with sample proportion hat p; observed statistics are evidence, not unknown claims.

Worked solution P61-Tough-3. Let p be the population proportion in context. Use $H_0:p=0.50$ and $H_a:p\ne 0.50$. The null contains equality because the reference distribution is computed under the specific value 0.50. Interpretation: Make the alpha comparison, state reject or fail to reject H0, and conclude in terms of evidence for the population claim. Validity: Choose direction from the research claim before seeing sample results and define p with population and success category. Error to reject: Do not write hypotheses with sample proportion hat p; observed statistics are evidence, not unknown claims.

Worked solution P61-Tough-4. Let p be the population proportion in context. Use $H_0:p=0.50$ and $H_a:p\>0.50$. The null contains equality because the reference distribution is computed under the specific value 0.50. Interpretation: Make the alpha comparison, state reject or fail to reject H0, and conclude in terms of evidence for the population claim. Validity: Choose direction from the research claim before seeing sample results and define p with population and success category. Error to reject: Do not write hypotheses with sample proportion hat p; observed statistics are evidence, not unknown claims.

Worked solution P61-Tough-5. Let p be the population proportion in context. Use $H_0:p=0.50$ and $H_a:p\<0.50$. The null contains equality because the reference distribution is computed under the specific value 0.50. Interpretation: Make the alpha comparison, state reject or fail to reject H0, and conclude in terms of evidence for the population claim. Validity: Choose direction from the research claim before seeing sample results and define p with population and success category. Error to reject: Do not write hypotheses with sample proportion hat p; observed statistics are evidence, not unknown claims.

Worked solution P61-Tough-6. Let p be the population proportion in context. Use $H_0:p=0.50$ and $H_a:p\ne 0.50$. The null contains equality because the reference distribution is computed under the specific value 0.50. Interpretation: Make the alpha comparison, state reject or fail to reject H0, and conclude in terms of evidence for the population claim. Validity: Choose direction from the research claim before seeing sample results and define p with population and success category. Error to reject: Do not write hypotheses with sample proportion hat p; observed statistics are evidence, not unknown claims.

Worked solution P61-Tough-7. Let p be the population proportion in context. Use $H_0:p=0.50$ and $H_a:p\>0.50$. The null contains equality because the reference distribution is computed under the specific value 0.50. Interpretation: Make the alpha comparison, state reject or fail to reject H0, and conclude in terms of evidence for the population claim. Validity: Choose direction from the research claim before seeing sample results and define p with population and success category. Error to reject: Do not write hypotheses with sample proportion hat p; observed statistics are evidence, not unknown claims.

Worked solution P61-Tough-8. Let p be the population proportion in context. Use $H_0:p=0.50$ and $H_a:p\<0.50$. The null contains equality because the reference distribution is computed under the specific value 0.50. Interpretation: Make the alpha comparison, state reject or fail to reject H0, and conclude in terms of evidence for the population claim. Validity: Choose direction from the research claim before seeing sample results and define p with population and success category. Error to reject: Do not write hypotheses with sample proportion hat p; observed statistics are evidence, not unknown claims.

Worked solution P61-Tough-9. Let p be the population proportion in context. Use $H_0:p=0.50$ and $H_a:p\ne 0.50$. The null contains equality because the reference distribution is computed under the specific value 0.50. Interpretation: Make the alpha comparison, state reject or fail to reject H0, and conclude in terms of evidence for the population claim. Validity: Choose direction from the research claim before seeing sample results and define p with population and success category. Error to reject: Do not write hypotheses with sample proportion hat p; observed statistics are evidence, not unknown claims.

Worked solution P61-Tough-10. Let p be the population proportion in context. Use $H_0:p=0.50$ and $H_a:p\>0.50$. The null contains equality because the reference distribution is computed under the specific value 0.50. Interpretation: Make the alpha comparison, state reject or fail to reject H0, and conclude in terms of evidence for the population claim. Validity: Choose direction from the research claim before seeing sample results and define p with population and success category. Error to reject: Do not write hypotheses with sample proportion hat p; observed statistics are evidence, not unknown claims.

Worked solution P61-Tough-11. Let p be the population proportion in context. Use $H_0:p=0.50$ and $H_a:p\<0.50$. The null contains equality because the reference distribution is computed under the specific value 0.50. Interpretation: Make the alpha comparison, state reject or fail to reject H0, and conclude in terms of evidence for the population claim. Validity: Choose direction from the research claim before seeing sample results and define p with population and success category. Error to reject: Do not write hypotheses with sample proportion hat p; observed statistics are evidence, not unknown claims.

Worked solution P61-Tough-12. Let p be the population proportion in context. Use $H_0:p=0.50$ and $H_a:p\ne 0.50$. The null contains equality because the reference distribution is computed under the specific value 0.50. Interpretation: Make the alpha comparison, state reject or fail to reject H0, and conclude in terms of evidence for the population claim. Validity: Choose direction from the research claim before seeing sample results and define p with population and success category. Error to reject: Do not write hypotheses with sample proportion hat p; observed statistics are evidence, not unknown claims.

Worked solution P61-Tough-13. Let p be the population proportion in context. Use $H_0:p=0.50$ and $H_a:p\>0.50$. The null contains equality because the reference distribution is computed under the specific value 0.50. Interpretation: Make the alpha comparison, state reject or fail to reject H0, and conclude in terms of evidence for the population claim. Validity: Choose direction from the research claim before seeing sample results and define p with population and success category. Error to reject: Do not write hypotheses with sample proportion hat p; observed statistics are evidence, not unknown claims.

Worked solution P61-Tough-14. Let p be the population proportion in context. Use $H_0:p=0.50$ and $H_a:p\<0.50$. The null contains equality because the reference distribution is computed under the specific value 0.50. Interpretation: Make the alpha comparison, state reject or fail to reject H0, and conclude in terms of evidence for the population claim. Validity: Choose direction from the research claim before seeing sample results and define p with population and success category. Error to reject: Do not write hypotheses with sample proportion hat p; observed statistics are evidence, not unknown claims.

Worked solution P61-Tough-15. Let p be the population proportion in context. Use $H_0:p=0.50$ and $H_a:p\ne 0.50$. The null contains equality because the reference distribution is computed under the specific value 0.50. Interpretation: Make the alpha comparison, state reject or fail to reject H0, and conclude in terms of evidence for the population claim. Validity: Choose direction from the research claim before seeing sample results and define p with population and success category. Error to reject: Do not write hypotheses with sample proportion hat p; observed statistics are evidence, not unknown claims.

Worked solution P61-Tough-16. Let p be the population proportion in context. Use $H_0:p=0.50$ and $H_a:p\>0.50$. The null contains equality because the reference distribution is computed under the specific value 0.50. Interpretation: Make the alpha comparison, state reject or fail to reject H0, and conclude in terms of evidence for the population claim. Validity: Choose direction from the research claim before seeing sample results and define p with population and success category. Error to reject: Do not write hypotheses with sample proportion hat p; observed statistics are evidence, not unknown claims.

Worked solution P61-Toughest-1. Let p be the population proportion in context. Use $H_0:p=0.50$ and $H_a:p\>0.50$. The null contains equality because the reference distribution is computed under the specific value 0.50. Interpretation: Make the alpha comparison, state reject or fail to reject H0, and conclude in terms of evidence for the population claim. Validity: Choose direction from the research claim before seeing sample results and define p with population and success category. Error to reject: Do not write hypotheses with sample proportion hat p; observed statistics are evidence, not unknown claims.

Worked solution P61-Toughest-2. Let p be the population proportion in context. Use $H_0:p=0.50$ and $H_a:p\<0.50$. The null contains equality because the reference distribution is computed under the specific value 0.50. Interpretation: Make the alpha comparison, state reject or fail to reject H0, and conclude in terms of evidence for the population claim. Validity: Choose direction from the research claim before seeing sample results and define p with population and success category. Error to reject: Do not write hypotheses with sample proportion hat p; observed statistics are evidence, not unknown claims.

Worked solution P61-Toughest-3. Let p be the population proportion in context. Use $H_0:p=0.50$ and $H_a:p\ne 0.50$. The null contains equality because the reference distribution is computed under the specific value 0.50. Interpretation: Make the alpha comparison, state reject or fail to reject H0, and conclude in terms of evidence for the population claim. Validity: Choose direction from the research claim before seeing sample results and define p with population and success category. Error to reject: Do not write hypotheses with sample proportion hat p; observed statistics are evidence, not unknown claims.

Worked solution P61-Toughest-4. Let p be the population proportion in context. Use $H_0:p=0.50$ and $H_a:p\>0.50$. The null contains equality because the reference distribution is computed under the specific value 0.50. Interpretation: Make the alpha comparison, state reject or fail to reject H0, and conclude in terms of evidence for the population claim. Validity: Choose direction from the research claim before seeing sample results and define p with population and success category. Error to reject: Do not write hypotheses with sample proportion hat p; observed statistics are evidence, not unknown claims.

Worked solution P61-Toughest-5. Let p be the population proportion in context. Use $H_0:p=0.50$ and $H_a:p\<0.50$. The null contains equality because the reference distribution is computed under the specific value 0.50. Interpretation: Make the alpha comparison, state reject or fail to reject H0, and conclude in terms of evidence for the population claim. Validity: Choose direction from the research claim before seeing sample results and define p with population and success category. Error to reject: Do not write hypotheses with sample proportion hat p; observed statistics are evidence, not unknown claims.

Worked solution P61-Toughest-6. Let p be the population proportion in context. Use $H_0:p=0.50$ and $H_a:p\ne 0.50$. The null contains equality because the reference distribution is computed under the specific value 0.50. Interpretation: Make the alpha comparison, state reject or fail to reject H0, and conclude in terms of evidence for the population claim. Validity: Choose direction from the research claim before seeing sample results and define p with population and success category. Error to reject: Do not write hypotheses with sample proportion hat p; observed statistics are evidence, not unknown claims.

Worked solution P61-Toughest-7. Let p be the population proportion in context. Use $H_0:p=0.50$ and $H_a:p\>0.50$. The null contains equality because the reference distribution is computed under the specific value 0.50. Interpretation: Make the alpha comparison, state reject or fail to reject H0, and conclude in terms of evidence for the population claim. Validity: Choose direction from the research claim before seeing sample results and define p with population and success category. Error to reject: Do not write hypotheses with sample proportion hat p; observed statistics are evidence, not unknown claims.

Worked solution P61-Toughest-8. Let p be the population proportion in context. Use $H_0:p=0.50$ and $H_a:p\<0.50$. The null contains equality because the reference distribution is computed under the specific value 0.50. Interpretation: Make the alpha comparison, state reject or fail to reject H0, and conclude in terms of evidence for the population claim. Validity: Choose direction from the research claim before seeing sample results and define p with population and success category. Error to reject: Do not write hypotheses with sample proportion hat p; observed statistics are evidence, not unknown claims.

Worked solution P61-Toughest-9. Let p be the population proportion in context. Use $H_0:p=0.50$ and $H_a:p\ne 0.50$. The null contains equality because the reference distribution is computed under the specific value 0.50. Interpretation: Make the alpha comparison, state reject or fail to reject H0, and conclude in terms of evidence for the population claim. Validity: Choose direction from the research claim before seeing sample results and define p with population and success category. Error to reject: Do not write hypotheses with sample proportion hat p; observed statistics are evidence, not unknown claims.

Worked solution P61-Toughest-10. Let p be the population proportion in context. Use $H_0:p=0.50$ and $H_a:p\>0.50$. The null contains equality because the reference distribution is computed under the specific value 0.50. Interpretation: Make the alpha comparison, state reject or fail to reject H0, and conclude in terms of evidence for the population claim. Validity: Choose direction from the research claim before seeing sample results and define p with population and success category. Error to reject: Do not write hypotheses with sample proportion hat p; observed statistics are evidence, not unknown claims.

Worked solution P61-Toughest-11. Let p be the population proportion in context. Use $H_0:p=0.50$ and $H_a:p\<0.50$. The null contains equality because the reference distribution is computed under the specific value 0.50. Interpretation: Make the alpha comparison, state reject or fail to reject H0, and conclude in terms of evidence for the population claim. Validity: Choose direction from the research claim before seeing sample results and define p with population and success category. Error to reject: Do not write hypotheses with sample proportion hat p; observed statistics are evidence, not unknown claims.

Worked solution P61-Toughest-12. Let p be the population proportion in context. Use $H_0:p=0.50$ and $H_a:p\ne 0.50$. The null contains equality because the reference distribution is computed under the specific value 0.50. Interpretation: Make the alpha comparison, state reject or fail to reject H0, and conclude in terms of evidence for the population claim. Validity: Choose direction from the research claim before seeing sample results and define p with population and success category. Error to reject: Do not write hypotheses with sample proportion hat p; observed statistics are evidence, not unknown claims.

Worked solution P61-Toughest-13. Let p be the population proportion in context. Use $H_0:p=0.50$ and $H_a:p\>0.50$. The null contains equality because the reference distribution is computed under the specific value 0.50. Interpretation: Make the alpha comparison, state reject or fail to reject H0, and conclude in terms of evidence for the population claim. Validity: Choose direction from the research claim before seeing sample results and define p with population and success category. Error to reject: Do not write hypotheses with sample proportion hat p; observed statistics are evidence, not unknown claims.

Worked solution P61-Toughest-14. Let p be the population proportion in context. Use $H_0:p=0.50$ and $H_a:p\<0.50$. The null contains equality because the reference distribution is computed under the specific value 0.50. Interpretation: Make the alpha comparison, state reject or fail to reject H0, and conclude in terms of evidence for the population claim. Validity: Choose direction from the research claim before seeing sample results and define p with population and success category. Error to reject: Do not write hypotheses with sample proportion hat p; observed statistics are evidence, not unknown claims.

Worked solution P61-Toughest-15. Let p be the population proportion in context. Use $H_0:p=0.50$ and $H_a:p\ne 0.50$. The null contains equality because the reference distribution is computed under the specific value 0.50. Interpretation: Make the alpha comparison, state reject or fail to reject H0, and conclude in terms of evidence for the population claim. Validity: Choose direction from the research claim before seeing sample results and define p with population and success category. Error to reject: Do not write hypotheses with sample proportion hat p; observed statistics are evidence, not unknown claims.

Worked solution P61-Toughest-16. Let p be the population proportion in context. Use $H_0:p=0.50$ and $H_a:p\>0.50$. The null contains equality because the reference distribution is computed under the specific value 0.50. Interpretation: Make the alpha comparison, state reject or fail to reject H0, and conclude in terms of evidence for the population claim. Validity: Choose direction from the research claim before seeing sample results and define p with population and success category. Error to reject: Do not write hypotheses with sample proportion hat p; observed statistics are evidence, not unknown claims.