7.4 Proportions and Critical Values

Use for question 2-6:

A study found that 68% of the population owns a home. In a random sample of 150 households, 92 owned a home. At the α = 0.01 level, is there enough evidence to reject the claim?

Choose the correct hypotheses.

• H₀: p = 0.68

  H_a: p ≠ 0.68

• H₀: μ = 0.68

  H_a: μ ≠ 0.68

A study found that 68% of the population owns a home. In a random sample of 150 households, 92 owned a home. At the α = 0.01 level, is there enough evidence to reject the claim?

Find the z-score.

• z = -1.75

• z = 1.75

• z = -0.08

• z = 0.08

A study found that 68% of the population owns a home. In a random sample of 150 households, 92 owned a home. At the α = 0.01 level, is there enough evidence to reject the claim?

Which value is closest to the p-value?

• 0.02

• 0.04

• 0.06

• 0.08

A study found that 68% of the population owns a home. In a random sample of 150 households, 92 owned a home. At the α = 0.01 level, is there enough evidence to reject the claim?

What is the correct conclusion?

• Fail to reject the null hypothesis

• Reject the null hypothesis

A study found that 68% of the population owns a home. In a random sample of 150 households, 92 owned a home. At the α = 0.01 level, is there enough evidence to reject the claim?

• There is not enough evidence to reject the claim that 68% of the population owns a home

• There is enough evidence to reject the claim that 68% of the population owns a home

Use for question 7-11:

The percentage of female physicians is 27%. In a survey of physicians, 45 of the 120 were women. Is there sufficient evidence at the α = 0.01 to claim that the proportion of women physicians is greater than 27%?

Choose the correct hypotheses.

• H₀: p = 0.27

  H_a: p > 0.27

• H₀: p = 0.27

  H_a: p < 0.27

• H₀: p = 0.27

  H_a: p ≠ 0.27

• H₀: p > 0.27

  H_a: p = 0.27

The percentage of female physicians is 27%. In a survey of physicians, 45 of the 120 were women. Is there sufficient evidence at the α = 0.01 to claim that the proportion of women physicians is greater than 27%?

Find the z-score.

• z = -2.59

• z = -0.005

• z = 2.59

• z = 0.005

The percentage of female physicians is 27%. In a survey of physicians, 45 of the 120 were women. Is there sufficient evidence at the α = 0.01 to claim that the proportion of women physicians is greater than 27%?

Which is closest to the p-value?

• 0.0005

• 0.005

• 0.05

• 0.5

The percentage of female physicians is 27%. In a survey of physicians, 45 of the 120 were women. Is there sufficient evidence at the α = 0.01 to claim that the proportion of women physicians is greater than 27%?

What is the correct conclusion?

• Fail to reject the null hypothesis

• Reject the null hypothesis

The percentage of female physicians is 27%. In a survey of physicians, 45 of the 120 were women. Is there sufficient evidence at the α = 0.01 to claim that the proportion of women physicians is greater than 27%?

• There is not enough evidence to support the claim that the proportion of women physicians is greater than 27%

• There is enough evidence to support the claim that the proportion of women physicians is greater than 27%