Hypothesis Testing for proportions

Which of the following represents the appropriate null & alternative hypotheses?

The mean height of women is greater than 64"

• H₀: μ > 64"

  Hₐ: μ ≠ 64"

• H₀: μ < 64"

  Hₐ: μ > 64"

• H₀: p > 64"

  Hₐ: p ≠ 64"

• H₀: p = 64"

  Hₐ: p > 64"

Tags

CCSS.HSS.IC.A.1

Identify the correct null hypothesis:

Is the proportion of babies born male different from 50%? In a sample of 200 babies, 96 were male. Test the claim using a level of significance of 1%.

• H₀: p = 0.50

• H₀: µ = 100

• H₀: p = 0.48

• H₀: µ = 96

Tags

CCSS.HSS.IC.A.1

CCSS.HSS.IC.B.4

CCSS.HSS.ID.A.4

CCSS.HSS.ID.B.5

A mayor is concerned about the percentage of city residents who express disapproval of his job performance. His political committee pays for a newspaper ad, hoping to keep his disapproval rating below 21%. They will use a follow up poll to access effectiveness. What are the correct null and alternative hypotheses?

• Ho: μ > 21

  Ha: μ < 21

• Ho: p > .20

  Ha: p < .20

• Ho: p < .21

  Ha: p > .21

• Ho: p > .21

  Ha: p < .21

On average, 86% of all enrolled college students are undergraduates. A random sample of 500 college students revealed that 420 were undergraduates. At α = 0.10 level, is there enough evidence to conclude that the proportion is lower than the national average?

Choose the correct hypotheses.

• H₀: p >= 0.86

  H_a: p < 0.86

• H₀: p <= 0.86

  H_a: p > 0.86

• H₀: p = 0.86

  H_a: p ≠ 0.86

• H₀: p < 0.86

  H_a: p >= 0.86

Tags

CCSS.HSS.IC.A.1

CCSS.HSS.IC.B.4

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

Tags

CCSS.HSS.IC.A.1

CCSS.HSS.IC.B.3

CCSS.HSS.IC.B.4

CCSS.HSS.ID.A.4

CCSS.HSS.ID.B.5

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

Tags

CCSS.HSS.IC.A.1

CCSS.HSS.IC.B.4

• Fail to Reject the null, there is not a significant difference.

• Reject undefined, there is NOT a significant difference

• Accept undefined, there is a significant difference

Tags

CCSS.HSS.IC.A.1

Which of the following is not an option for an alternative hypothesis?

• H_a = k

• H_a > k

• H_a < k

• H_a ≠ k

Tags

CCSS.HSS.IC.B.5

Suppose the P-value for a hypothesis test is 0.0304. Using α = 0.05, what is the appropriate conclusion?

• Reject the null hypothesis

• Reject the alternative hypothesis

• Fail to reject the null hypothesis

• Fail to reject the alternative hypothesis

Tags

CCSS.HSS.ID.A.4

5% of trucks of a certain model have needed new engines after being driven between 0 and 100 miles.  The manufacturer hopes that the redesign of one of the engine's components has solved this problem.  Write the null and alternative hypotheses for this situation.

• Ho:  p < 0.05
  Ha:  p >= 0.05

• Ho:  p <= 0.05
  Ha:  p > 0.05

• Ho:  p >= 0.05
  Ha:  p < 0.05

• Ho:  p > 0.05
  Ha:  p = 0.05

Tags

CCSS.HSS.IC.B.5