Probability and Statistics Formative Assessment 7.1

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"

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

•   a)  reject the null
• b)  reject the alternative
• c)  Accept the null
• d)  Fail to reject the alternative

In their advertisements, a new diet program would like to claim that their methods result in a mean weight loss of more than ten pounds in two weeks. In order to determine if this is a valid claim, they hire an independent testing agency that then selects twenty-five people to be placed on this diet. The agency should be testing the null hypothesis H₀: m = 10 and the alternative hypothesis

• Ha: μ < 10
• Ha: μ > 10
• Ha: μ ≥ 10
• Ha: μ ≤ 10

Tags

CCSS.HSS.IC.A.1

CCSS.HSS.IC.B.4

CCSS.HSS.IC.B.5

A car manufacturer advertises that its new subcompact models get an mean of 47 mpg. If μ is the mileage of these cars, what could be the null and alternate hypothesis if we wanted to check if the car's mpg is overrated?

• H₀ p= 47

  H_a p= 47

• H₀ μ = 47

  H_a μ < 47

• Ha p= 47

  H_a p> 47

• Ha μ = 47

  H_a μ ≠ 47

Which of the following best describes a Type I error?

• The null is true, but we mistakenly reject it.
• The null is false and we reject it.
• The null is false, but we fail to reject it.
• The null is true but we fail to reject it.

Tags

CCSS.HSS.MD.B.7

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

Which of the following shows a right-tailed test?

• Ha: µ < 15

• H₀: µ < 15

• Ha: µ > 15

• H₀: µ > 15

Identify the correct null hypothesis:

• H₀: p = 0.50

• H₀: μ = 100

• H₀: p = 0.48

• H₀: μ = 96

What is the only option for the null hypothesis? 

• H₀ = k
• H₀ > k
• H₀ < k
• H₀ ≠ k

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.A.1

CCSS.HSS.IC.B.4