Worked solution P60-Easy-1. The test statistic is z=2.535 and the two-sided p-value is 0.0112. $$z=\frac{0.6071-0.50}{\sqrt{0.50(0.50)/140}}=2.535.$$ Interpretation: Make the alpha comparison, state reject or fail to reject H0, and conclude in terms of evidence for the population claim. Validity: Check randomization, independence, and null large counts $n{p}_0\ge 10$ and $n(1-p_0)\ge 10$. Error to reject: A small p-value is evidence against H0, not proof that the alternative is true or practically important.

Worked solution P60-Easy-2. The test statistic is z=1.263 and the two-sided p-value is 0.2065. $$z=\frac{0.5532-0.50}{\sqrt{0.50(0.50)/141}}=1.263.$$ Interpretation: Make the alpha comparison, state reject or fail to reject H0, and conclude in terms of evidence for the population claim. Validity: Check randomization, independence, and null large counts $n{p}_0\ge 10$ and $n(1-p_0)\ge 10$. Error to reject: A small p-value is evidence against H0, not proof that the alternative is true or practically important.

Worked solution P60-Easy-3. The test statistic is z=1.007 and the two-sided p-value is 0.3139. $$z=\frac{0.5423-0.50}{\sqrt{0.50(0.50)/142}}=1.007.$$ Interpretation: Make the alpha comparison, state reject or fail to reject H0, and conclude in terms of evidence for the population claim. Validity: Check randomization, independence, and null large counts $n{p}_0\ge 10$ and $n(1-p_0)\ge 10$. Error to reject: A small p-value is evidence against H0, not proof that the alternative is true or practically important.

Worked solution P60-Easy-4. The test statistic is z=2.927 and the two-sided p-value is 0.0034. $$z=\frac{0.6224-0.50}{\sqrt{0.50(0.50)/143}}=2.927.$$ Interpretation: Make the alpha comparison, state reject or fail to reject H0, and conclude in terms of evidence for the population claim. Validity: Check randomization, independence, and null large counts $n{p}_0\ge 10$ and $n(1-p_0)\ge 10$. Error to reject: A small p-value is evidence against H0, not proof that the alternative is true or practically important.

Worked solution P60-Easy-5. The test statistic is z=0.667 and the two-sided p-value is 0.5050. $$z=\frac{0.5278-0.50}{\sqrt{0.50(0.50)/144}}=0.667.$$ Interpretation: Make the alpha comparison, state reject or fail to reject H0, and conclude in terms of evidence for the population claim. Validity: Check randomization, independence, and null large counts $n{p}_0\ge 10$ and $n(1-p_0)\ge 10$. Error to reject: A small p-value is evidence against H0, not proof that the alternative is true or practically important.

Worked solution P60-Easy-6. The test statistic is z=2.574 and the two-sided p-value is 0.0100. $$z=\frac{0.6069-0.50}{\sqrt{0.50(0.50)/145}}=2.574.$$ Interpretation: Make the alpha comparison, state reject or fail to reject H0, and conclude in terms of evidence for the population claim. Validity: Check randomization, independence, and null large counts $n{p}_0\ge 10$ and $n(1-p_0)\ge 10$. Error to reject: A small p-value is evidence against H0, not proof that the alternative is true or practically important.

Worked solution P60-Easy-7. The test statistic is z=0.662 and the two-sided p-value is 0.5079. $$z=\frac{0.5274-0.50}{\sqrt{0.50(0.50)/146}}=0.662.$$ Interpretation: Make the alpha comparison, state reject or fail to reject H0, and conclude in terms of evidence for the population claim. Validity: Check randomization, independence, and null large counts $n{p}_0\ge 10$ and $n(1-p_0)\ge 10$. Error to reject: A small p-value is evidence against H0, not proof that the alternative is true or practically important.

Worked solution P60-Easy-8. The test statistic is z=1.402 and the two-sided p-value is 0.1609. $$z=\frac{0.5578-0.50}{\sqrt{0.50(0.50)/147}}=1.402.$$ Interpretation: Make the alpha comparison, state reject or fail to reject H0, and conclude in terms of evidence for the population claim. Validity: Check randomization, independence, and null large counts $n{p}_0\ge 10$ and $n(1-p_0)\ge 10$. Error to reject: A small p-value is evidence against H0, not proof that the alternative is true or practically important.

Worked solution P60-Easy-9. The test statistic is z=3.452 and the two-sided p-value is 0.0006. $$z=\frac{0.6419-0.50}{\sqrt{0.50(0.50)/148}}=3.452.$$ Interpretation: Make the alpha comparison, state reject or fail to reject H0, and conclude in terms of evidence for the population claim. Validity: Check randomization, independence, and null large counts $n{p}_0\ge 10$ and $n(1-p_0)\ge 10$. Error to reject: A small p-value is evidence against H0, not proof that the alternative is true or practically important.

Worked solution P60-Easy-10. The test statistic is z=0.901 and the two-sided p-value is 0.3675. $$z=\frac{0.5369-0.50}{\sqrt{0.50(0.50)/149}}=0.901.$$ Interpretation: Make the alpha comparison, state reject or fail to reject H0, and conclude in terms of evidence for the population claim. Validity: Check randomization, independence, and null large counts $n{p}_0\ge 10$ and $n(1-p_0)\ge 10$. Error to reject: A small p-value is evidence against H0, not proof that the alternative is true or practically important.

Worked solution P60-Easy-11. The test statistic is z=0.816 and the two-sided p-value is 0.4142. $$z=\frac{0.5333-0.50}{\sqrt{0.50(0.50)/150}}=0.816.$$ Interpretation: Make the alpha comparison, state reject or fail to reject H0, and conclude in terms of evidence for the population claim. Validity: Check randomization, independence, and null large counts $n{p}_0\ge 10$ and $n(1-p_0)\ge 10$. Error to reject: A small p-value is evidence against H0, not proof that the alternative is true or practically important.

Worked solution P60-Easy-12. The test statistic is z=3.011 and the two-sided p-value is 0.0026. $$z=\frac{0.6225-0.50}{\sqrt{0.50(0.50)/151}}=3.011.$$ Interpretation: Make the alpha comparison, state reject or fail to reject H0, and conclude in terms of evidence for the population claim. Validity: Check randomization, independence, and null large counts $n{p}_0\ge 10$ and $n(1-p_0)\ge 10$. Error to reject: A small p-value is evidence against H0, not proof that the alternative is true or practically important.

Worked solution P60-Easy-13. The test statistic is z=1.784 and the two-sided p-value is 0.0744. $$z=\frac{0.5724-0.50}{\sqrt{0.50(0.50)/152}}=1.784.$$ Interpretation: Make the alpha comparison, state reject or fail to reject H0, and conclude in terms of evidence for the population claim. Validity: Check randomization, independence, and null large counts $n{p}_0\ge 10$ and $n(1-p_0)\ge 10$. Error to reject: A small p-value is evidence against H0, not proof that the alternative is true or practically important.

Worked solution P60-Easy-14. The test statistic is z=3.153 and the two-sided p-value is 0.0016. $$z=\frac{0.6275-0.50}{\sqrt{0.50(0.50)/153}}=3.153.$$ Interpretation: Make the alpha comparison, state reject or fail to reject H0, and conclude in terms of evidence for the population claim. Validity: Check randomization, independence, and null large counts $n{p}_0\ge 10$ and $n(1-p_0)\ge 10$. Error to reject: A small p-value is evidence against H0, not proof that the alternative is true or practically important.

Worked solution P60-Easy-15. The test statistic is z=3.546 and the two-sided p-value is 0.0004. $$z=\frac{0.6429-0.50}{\sqrt{0.50(0.50)/154}}=3.546.$$ Interpretation: Make the alpha comparison, state reject or fail to reject H0, and conclude in terms of evidence for the population claim. Validity: Check randomization, independence, and null large counts $n{p}_0\ge 10$ and $n(1-p_0)\ge 10$. Error to reject: A small p-value is evidence against H0, not proof that the alternative is true or practically important.

Worked solution P60-Easy-16. The test statistic is z=1.687 and the two-sided p-value is 0.0916. $$z=\frac{0.5677-0.50}{\sqrt{0.50(0.50)/155}}=1.687.$$ Interpretation: Make the alpha comparison, state reject or fail to reject H0, and conclude in terms of evidence for the population claim. Validity: Check randomization, independence, and null large counts $n{p}_0\ge 10$ and $n(1-p_0)\ge 10$. Error to reject: A small p-value is evidence against H0, not proof that the alternative is true or practically important.

Worked solution P60-Easy-17. The test statistic is z=2.722 and the two-sided p-value is 0.0065. $$z=\frac{0.6090-0.50}{\sqrt{0.50(0.50)/156}}=2.722.$$ Interpretation: Make the alpha comparison, state reject or fail to reject H0, and conclude in terms of evidence for the population claim. Validity: Check randomization, independence, and null large counts $n{p}_0\ge 10$ and $n(1-p_0)\ge 10$. Error to reject: A small p-value is evidence against H0, not proof that the alternative is true or practically important.

Worked solution P60-Tough-1. The test statistic is z=1.352 and the two-sided p-value is 0.1763. $$z=\frac{0.5571-0.50}{\sqrt{0.50(0.50)/140}}=1.352.$$ Interpretation: Make the alpha comparison, state reject or fail to reject H0, and conclude in terms of evidence for the population claim. Validity: Check randomization, independence, and null large counts $n{p}_0\ge 10$ and $n(1-p_0)\ge 10$. Error to reject: A small p-value is evidence against H0, not proof that the alternative is true or practically important.

Worked solution P60-Tough-2. The test statistic is z=2.611 and the two-sided p-value is 0.0090. $$z=\frac{0.6099-0.50}{\sqrt{0.50(0.50)/141}}=2.611.$$ Interpretation: Make the alpha comparison, state reject or fail to reject H0, and conclude in terms of evidence for the population claim. Validity: Check randomization, independence, and null large counts $n{p}_0\ge 10$ and $n(1-p_0)\ge 10$. Error to reject: A small p-value is evidence against H0, not proof that the alternative is true or practically important.

Worked solution P60-Tough-3. The test statistic is z=2.182 and the two-sided p-value is 0.0291. $$z=\frac{0.5915-0.50}{\sqrt{0.50(0.50)/142}}=2.182.$$ Interpretation: Make the alpha comparison, state reject or fail to reject H0, and conclude in terms of evidence for the population claim. Validity: Check randomization, independence, and null large counts $n{p}_0\ge 10$ and $n(1-p_0)\ge 10$. Error to reject: A small p-value is evidence against H0, not proof that the alternative is true or practically important.

Worked solution P60-Tough-4. The test statistic is z=2.091 and the two-sided p-value is 0.0366. $$z=\frac{0.5874-0.50}{\sqrt{0.50(0.50)/143}}=2.091.$$ Interpretation: Make the alpha comparison, state reject or fail to reject H0, and conclude in terms of evidence for the population claim. Validity: Check randomization, independence, and null large counts $n{p}_0\ge 10$ and $n(1-p_0)\ge 10$. Error to reject: A small p-value is evidence against H0, not proof that the alternative is true or practically important.

Worked solution P60-Tough-5. The test statistic is z=2.667 and the two-sided p-value is 0.0077. $$z=\frac{0.6111-0.50}{\sqrt{0.50(0.50)/144}}=2.667.$$ Interpretation: Make the alpha comparison, state reject or fail to reject H0, and conclude in terms of evidence for the population claim. Validity: Check randomization, independence, and null large counts $n{p}_0\ge 10$ and $n(1-p_0)\ge 10$. Error to reject: A small p-value is evidence against H0, not proof that the alternative is true or practically important.

Worked solution P60-Tough-6. The test statistic is z=3.405 and the two-sided p-value is 0.0007. $$z=\frac{0.6414-0.50}{\sqrt{0.50(0.50)/145}}=3.405.$$ Interpretation: Make the alpha comparison, state reject or fail to reject H0, and conclude in terms of evidence for the population claim. Validity: Check randomization, independence, and null large counts $n{p}_0\ge 10$ and $n(1-p_0)\ge 10$. Error to reject: A small p-value is evidence against H0, not proof that the alternative is true or practically important.

Worked solution P60-Tough-7. The test statistic is z=3.310 and the two-sided p-value is 0.0009. $$z=\frac{0.6370-0.50}{\sqrt{0.50(0.50)/146}}=3.310.$$ Interpretation: Make the alpha comparison, state reject or fail to reject H0, and conclude in terms of evidence for the population claim. Validity: Check randomization, independence, and null large counts $n{p}_0\ge 10$ and $n(1-p_0)\ge 10$. Error to reject: A small p-value is evidence against H0, not proof that the alternative is true or practically important.

Worked solution P60-Tough-8. The test statistic is z=2.392 and the two-sided p-value is 0.0168. $$z=\frac{0.5986-0.50}{\sqrt{0.50(0.50)/147}}=2.392.$$ Interpretation: Make the alpha comparison, state reject or fail to reject H0, and conclude in terms of evidence for the population claim. Validity: Check randomization, independence, and null large counts $n{p}_0\ge 10$ and $n(1-p_0)\ge 10$. Error to reject: A small p-value is evidence against H0, not proof that the alternative is true or practically important.

Worked solution P60-Tough-9. The test statistic is z=0.986 and the two-sided p-value is 0.3239. $$z=\frac{0.5405-0.50}{\sqrt{0.50(0.50)/148}}=0.986.$$ Interpretation: Make the alpha comparison, state reject or fail to reject H0, and conclude in terms of evidence for the population claim. Validity: Check randomization, independence, and null large counts $n{p}_0\ge 10$ and $n(1-p_0)\ge 10$. Error to reject: A small p-value is evidence against H0, not proof that the alternative is true or practically important.

Worked solution P60-Tough-10. The test statistic is z=1.720 and the two-sided p-value is 0.0854. $$z=\frac{0.5705-0.50}{\sqrt{0.50(0.50)/149}}=1.720.$$ Interpretation: Make the alpha comparison, state reject or fail to reject H0, and conclude in terms of evidence for the population claim. Validity: Check randomization, independence, and null large counts $n{p}_0\ge 10$ and $n(1-p_0)\ge 10$. Error to reject: A small p-value is evidence against H0, not proof that the alternative is true or practically important.

Worked solution P60-Tough-11. The test statistic is z=2.776 and the two-sided p-value is 0.0055. $$z=\frac{0.6133-0.50}{\sqrt{0.50(0.50)/150}}=2.776.$$ Interpretation: Make the alpha comparison, state reject or fail to reject H0, and conclude in terms of evidence for the population claim. Validity: Check randomization, independence, and null large counts $n{p}_0\ge 10$ and $n(1-p_0)\ge 10$. Error to reject: A small p-value is evidence against H0, not proof that the alternative is true or practically important.

Worked solution P60-Tough-12. The test statistic is z=2.523 and the two-sided p-value is 0.0116. $$z=\frac{0.6026-0.50}{\sqrt{0.50(0.50)/151}}=2.523.$$ Interpretation: Make the alpha comparison, state reject or fail to reject H0, and conclude in terms of evidence for the population claim. Validity: Check randomization, independence, and null large counts $n{p}_0\ge 10$ and $n(1-p_0)\ge 10$. Error to reject: A small p-value is evidence against H0, not proof that the alternative is true or practically important.

Worked solution P60-Tough-13. The test statistic is z=2.920 and the two-sided p-value is 0.0035. $$z=\frac{0.6184-0.50}{\sqrt{0.50(0.50)/152}}=2.920.$$ Interpretation: Make the alpha comparison, state reject or fail to reject H0, and conclude in terms of evidence for the population claim. Validity: Check randomization, independence, and null large counts $n{p}_0\ge 10$ and $n(1-p_0)\ge 10$. Error to reject: A small p-value is evidence against H0, not proof that the alternative is true or practically important.

Worked solution P60-Tough-14. The test statistic is z=3.153 and the two-sided p-value is 0.0016. $$z=\frac{0.6275-0.50}{\sqrt{0.50(0.50)/153}}=3.153.$$ Interpretation: Make the alpha comparison, state reject or fail to reject H0, and conclude in terms of evidence for the population claim. Validity: Check randomization, independence, and null large counts $n{p}_0\ge 10$ and $n(1-p_0)\ge 10$. Error to reject: A small p-value is evidence against H0, not proof that the alternative is true or practically important.

Worked solution P60-Tough-15. The test statistic is z=1.450 and the two-sided p-value is 0.1469. $$z=\frac{0.5584-0.50}{\sqrt{0.50(0.50)/154}}=1.450.$$ Interpretation: Make the alpha comparison, state reject or fail to reject H0, and conclude in terms of evidence for the population claim. Validity: Check randomization, independence, and null large counts $n{p}_0\ge 10$ and $n(1-p_0)\ge 10$. Error to reject: A small p-value is evidence against H0, not proof that the alternative is true or practically important.

Worked solution P60-Tough-16. The test statistic is z=3.454 and the two-sided p-value is 0.0006. $$z=\frac{0.6387-0.50}{\sqrt{0.50(0.50)/155}}=3.454.$$ Interpretation: Make the alpha comparison, state reject or fail to reject H0, and conclude in terms of evidence for the population claim. Validity: Check randomization, independence, and null large counts $n{p}_0\ge 10$ and $n(1-p_0)\ge 10$. Error to reject: A small p-value is evidence against H0, not proof that the alternative is true or practically important.

Worked solution P60-Tough-17. The test statistic is z=0.801 and the two-sided p-value is 0.4233. $$z=\frac{0.5321-0.50}{\sqrt{0.50(0.50)/156}}=0.801.$$ Interpretation: Make the alpha comparison, state reject or fail to reject H0, and conclude in terms of evidence for the population claim. Validity: Check randomization, independence, and null large counts $n{p}_0\ge 10$ and $n(1-p_0)\ge 10$. Error to reject: A small p-value is evidence against H0, not proof that the alternative is true or practically important.

Worked solution P60-Toughest-1. The test statistic is z=2.874 and the two-sided p-value is 0.0041. $$z=\frac{0.6214-0.50}{\sqrt{0.50(0.50)/140}}=2.874.$$ Interpretation: Make the alpha comparison, state reject or fail to reject H0, and conclude in terms of evidence for the population claim. Validity: Check randomization, independence, and null large counts $n{p}_0\ge 10$ and $n(1-p_0)\ge 10$. Error to reject: A small p-value is evidence against H0, not proof that the alternative is true or practically important.

Worked solution P60-Toughest-2. The test statistic is z=2.779 and the two-sided p-value is 0.0055. $$z=\frac{0.6170-0.50}{\sqrt{0.50(0.50)/141}}=2.779.$$ Interpretation: Make the alpha comparison, state reject or fail to reject H0, and conclude in terms of evidence for the population claim. Validity: Check randomization, independence, and null large counts $n{p}_0\ge 10$ and $n(1-p_0)\ge 10$. Error to reject: A small p-value is evidence against H0, not proof that the alternative is true or practically important.

Worked solution P60-Toughest-3. The test statistic is z=1.511 and the two-sided p-value is 0.1309. $$z=\frac{0.5634-0.50}{\sqrt{0.50(0.50)/142}}=1.511.$$ Interpretation: Make the alpha comparison, state reject or fail to reject H0, and conclude in terms of evidence for the population claim. Validity: Check randomization, independence, and null large counts $n{p}_0\ge 10$ and $n(1-p_0)\ge 10$. Error to reject: A small p-value is evidence against H0, not proof that the alternative is true or practically important.

Worked solution P60-Toughest-4. The test statistic is z=2.425 and the two-sided p-value is 0.0153. $$z=\frac{0.6014-0.50}{\sqrt{0.50(0.50)/143}}=2.425.$$ Interpretation: Make the alpha comparison, state reject or fail to reject H0, and conclude in terms of evidence for the population claim. Validity: Check randomization, independence, and null large counts $n{p}_0\ge 10$ and $n(1-p_0)\ge 10$. Error to reject: A small p-value is evidence against H0, not proof that the alternative is true or practically important.

Worked solution P60-Toughest-5. The test statistic is z=1.500 and the two-sided p-value is 0.1336. $$z=\frac{0.5625-0.50}{\sqrt{0.50(0.50)/144}}=1.500.$$ Interpretation: Make the alpha comparison, state reject or fail to reject H0, and conclude in terms of evidence for the population claim. Validity: Check randomization, independence, and null large counts $n{p}_0\ge 10$ and $n(1-p_0)\ge 10$. Error to reject: A small p-value is evidence against H0, not proof that the alternative is true or practically important.

Worked solution P60-Toughest-6. The test statistic is z=2.408 and the two-sided p-value is 0.0160. $$z=\frac{0.6000-0.50}{\sqrt{0.50(0.50)/145}}=2.408.$$ Interpretation: Make the alpha comparison, state reject or fail to reject H0, and conclude in terms of evidence for the population claim. Validity: Check randomization, independence, and null large counts $n{p}_0\ge 10$ and $n(1-p_0)\ge 10$. Error to reject: A small p-value is evidence against H0, not proof that the alternative is true or practically important.

Worked solution P60-Toughest-7. The test statistic is z=1.986 and the two-sided p-value is 0.0470. $$z=\frac{0.5822-0.50}{\sqrt{0.50(0.50)/146}}=1.986.$$ Interpretation: Make the alpha comparison, state reject or fail to reject H0, and conclude in terms of evidence for the population claim. Validity: Check randomization, independence, and null large counts $n{p}_0\ge 10$ and $n(1-p_0)\ge 10$. Error to reject: A small p-value is evidence against H0, not proof that the alternative is true or practically important.

Worked solution P60-Toughest-8. The test statistic is z=3.217 and the two-sided p-value is 0.0013. $$z=\frac{0.6327-0.50}{\sqrt{0.50(0.50)/147}}=3.217.$$ Interpretation: Make the alpha comparison, state reject or fail to reject H0, and conclude in terms of evidence for the population claim. Validity: Check randomization, independence, and null large counts $n{p}_0\ge 10$ and $n(1-p_0)\ge 10$. Error to reject: A small p-value is evidence against H0, not proof that the alternative is true or practically important.

Worked solution P60-Toughest-9. The test statistic is z=2.137 and the two-sided p-value is 0.0326. $$z=\frac{0.5878-0.50}{\sqrt{0.50(0.50)/148}}=2.137.$$ Interpretation: Make the alpha comparison, state reject or fail to reject H0, and conclude in terms of evidence for the population claim. Validity: Check randomization, independence, and null large counts $n{p}_0\ge 10$ and $n(1-p_0)\ge 10$. Error to reject: A small p-value is evidence against H0, not proof that the alternative is true or practically important.

Worked solution P60-Toughest-10. The test statistic is z=2.376 and the two-sided p-value is 0.0175. $$z=\frac{0.5973-0.50}{\sqrt{0.50(0.50)/149}}=2.376.$$ Interpretation: Make the alpha comparison, state reject or fail to reject H0, and conclude in terms of evidence for the population claim. Validity: Check randomization, independence, and null large counts $n{p}_0\ge 10$ and $n(1-p_0)\ge 10$. Error to reject: A small p-value is evidence against H0, not proof that the alternative is true or practically important.

Worked solution P60-Toughest-11. The test statistic is z=1.796 and the two-sided p-value is 0.0724. $$z=\frac{0.5733-0.50}{\sqrt{0.50(0.50)/150}}=1.796.$$ Interpretation: Make the alpha comparison, state reject or fail to reject H0, and conclude in terms of evidence for the population claim. Validity: Check randomization, independence, and null large counts $n{p}_0\ge 10$ and $n(1-p_0)\ge 10$. Error to reject: A small p-value is evidence against H0, not proof that the alternative is true or practically important.

Worked solution P60-Toughest-12. The test statistic is z=1.221 and the two-sided p-value is 0.2222. $$z=\frac{0.5497-0.50}{\sqrt{0.50(0.50)/151}}=1.221.$$ Interpretation: Make the alpha comparison, state reject or fail to reject H0, and conclude in terms of evidence for the population claim. Validity: Check randomization, independence, and null large counts $n{p}_0\ge 10$ and $n(1-p_0)\ge 10$. Error to reject: A small p-value is evidence against H0, not proof that the alternative is true or practically important.

Worked solution P60-Toughest-13. The test statistic is z=3.244 and the two-sided p-value is 0.0012. $$z=\frac{0.6316-0.50}{\sqrt{0.50(0.50)/152}}=3.244.$$ Interpretation: Make the alpha comparison, state reject or fail to reject H0, and conclude in terms of evidence for the population claim. Validity: Check randomization, independence, and null large counts $n{p}_0\ge 10$ and $n(1-p_0)\ge 10$. Error to reject: A small p-value is evidence against H0, not proof that the alternative is true or practically important.

Worked solution P60-Toughest-14. The test statistic is z=0.728 and the two-sided p-value is 0.4669. $$z=\frac{0.5294-0.50}{\sqrt{0.50(0.50)/153}}=0.728.$$ Interpretation: Make the alpha comparison, state reject or fail to reject H0, and conclude in terms of evidence for the population claim. Validity: Check randomization, independence, and null large counts $n{p}_0\ge 10$ and $n(1-p_0)\ge 10$. Error to reject: A small p-value is evidence against H0, not proof that the alternative is true or practically important.

Worked solution P60-Toughest-15. The test statistic is z=2.256 and the two-sided p-value is 0.0241. $$z=\frac{0.5909-0.50}{\sqrt{0.50(0.50)/154}}=2.256.$$ Interpretation: Make the alpha comparison, state reject or fail to reject H0, and conclude in terms of evidence for the population claim. Validity: Check randomization, independence, and null large counts $n{p}_0\ge 10$ and $n(1-p_0)\ge 10$. Error to reject: A small p-value is evidence against H0, not proof that the alternative is true or practically important.

Worked solution P60-Toughest-16. The test statistic is z=1.687 and the two-sided p-value is 0.0916. $$z=\frac{0.5677-0.50}{\sqrt{0.50(0.50)/155}}=1.687.$$ Interpretation: Make the alpha comparison, state reject or fail to reject H0, and conclude in terms of evidence for the population claim. Validity: Check randomization, independence, and null large counts $n{p}_0\ge 10$ and $n(1-p_0)\ge 10$. Error to reject: A small p-value is evidence against H0, not proof that the alternative is true or practically important.

Worked solution P60-Toughest-17. The test statistic is z=2.722 and the two-sided p-value is 0.0065. $$z=\frac{0.6090-0.50}{\sqrt{0.50(0.50)/156}}=2.722.$$ Interpretation: Make the alpha comparison, state reject or fail to reject H0, and conclude in terms of evidence for the population claim. Validity: Check randomization, independence, and null large counts $n{p}_0\ge 10$ and $n(1-p_0)\ge 10$. Error to reject: A small p-value is evidence against H0, not proof that the alternative is true or practically important.