Lesson 8.3 Checkpoint

Jason reads a report that says 80% of U.S. high school students have a computer at home. He believes the proportion is smaller than 0.80 at his large rural high school. Jason chooses an SRS of 60 students and finds that 41 have a computer at home. He would like to carry out a test at the α = 0.05 significance level of H₀: p = 0.80 versus H_a: p < 0.80, where p = the proportion of all students at Jason's high school who have a computer at home. Check if the conditions for performing the significance test are met.

• Random? No

  Large Counts? Yes

• Both fails

• Random? Yes

  Large Counts? fails

• Random? SRS of 60 students

  Large Counts? np₀ = 60(0.80) = 48 ≥ 10 and n(1-p₀) = 60(0.20) = 12 ≥ 10

A recent report claimed that 13% of students typically walk to school. DeAnna thinks that the proportion is higher than 0.13 at her large elementary school. She surveys a random sample of 100 students and finds that 17 typically walk to school. DeAnna would like to carry out a test at the α = 0.05 significance level of H₀: p = 0.13 versus H_a: p > 0.13, where p = the proportion of all students at her elementary school who typically walk to school. Check if the conditions for performing the significance test are met.

• Random? No

  Large Counts? Yes

• Both fails

• Random? Yes

  Large Counts? fails

• Random? Random sample of 100 students

  Large Counts? np₀ = 100(0.13) = 13 ≥ 10 and n(1-p₀) = 100(0.87) = 87 ≥ 10

A college president says, "More than two-thirds of the alumni support my firing of Coach Boggs." The president's statement is based on 200 emails he has received from alumni in the past three months. The college's athletic director wants to perform a test of H₀: p = ⅔ versus H_a: p > ⅔, where p = the true proportion of the college's alumni who favor firing the coach. Check if the conditions for performing the significance test are met.

• Random? No, volunteer response sample

  Large Counts? Yes

• Both fails

• Random? Yes

  Large Counts? fails

• Random? Random sample of 100 students

  Large Counts? np₀ = 100(0.13) = 13 ≥ 10 and n(1-p₀) = 100(0.87) = 87 ≥ 10

You want to determine if a coin is fair. You toss it 10 times and record the proportion of tosses that land heads. You would like to perform a test of H₀: p = 0.5 versus H_a: p ≠ 0.5, where p = the true proportion of all tosses of the coin that would land heads. Check if the conditions for performing the significance test are met.

• Random? No, volunteer response sample

  Large Counts? Yes

• Both fails

• Random? Yes

  Large Counts? fails

• Random? Random sample of 100 students

  Large Counts? np₀ = 100(0.13) = 13 ≥ 10 and n(1-p₀) = 100(0.87) = 87 ≥ 10

Jason reads a report that says 80% of U.S. high school students have a computer at home. He believes the proportion is smaller than 0.80 at his large rural high school. Jason chooses an SRS of 60 students and finds that 41 have a computer at home. He would like to carry out a test at the α = 0.05 significance level of H₀: p = 0.80 versus H_a: p < 0.80, where p = the proportion of all students at Jason's high school who have a computer at home. Calculate the standardized test statistic.

• p̂ = 0.6833

• z = -2.26

• z = 2.26

• You can't calculate it.

A recent report claimed that 13% of students typically walk to school. DeAnna thinks that the proportion is higher than 0.13 at her large elementary school. She surveys a random sample of 100 students and finds that 17 typically walk to school. DeAnna would like to carry out a test at the α = 0.05 significance level of H₀: p = 0.13 versus H_a: p > 0.13, where p = the proportion of all students at her elementary school who typically walk to school. Calculate the standardized test statistic.

• p̂ = 0.17

• z = -1.19

• z = 1.19

• You can't calculate it.

A college president says, "More than two-thirds of the alumni support my firing of Coach Boggs." The president's statement is based on 200 emails he has received from alumni in the past three months. The college's athletic director wants to perform a test of H₀: p = ⅔ versus H_a: p > ⅔, where p = the true proportion of the college's alumni who favor firing the coach. Calculate the standardized test statistic.

• p̂ = 0.96

• z = -2.00

• z = 2.00

• You can't calculate it.

You want to determine if a coin is fair. You toss it 10 times and record the proportion of tosses that land heads. You would like to perform a test of H₀: p = 0.5 versus H_a: p ≠ 0.5, where p = the true proportion of all tosses of the coin that would land heads. Calculate the standardized test statistic.

• p̂ = 0.5733

• z = -1.27

• z = 1.27

• You can't calculate it.

Jason reads a report that says 80% of U.S. high school students have a computer at home. He believes the proportion is smaller than 0.80 at his large rural high school. Jason chooses an SRS of 60 students and finds that 41 have a computer at home. He would like to carry out a test at the α = 0.05 significance level of H₀: p = 0.80 versus H_a: p < 0.80, where p = the proportion of all students at Jason's high school who have a computer at home. Find the P-value.

• 0.0119

• -2.26

• 2.26

• 0.6833

A recent report claimed that 13% of students typically walk to school. DeAnna thinks that the proportion is higher than 0.13 at her large elementary school. She surveys a random sample of 100 students and finds that 17 typically walk to school. DeAnna would like to carry out a test at the α = 0.05 significance level of H₀: p = 0.13 versus H_a: p > 0.13, where p = the proportion of all students at her elementary school who typically walk to school. Find the P-value.

• 0.17

• 0.8830

• 1.19

• 0.117