AP Statistics Hypothesis Tests for Means

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"

A manufacturer claims that his tires last at least 40,000

miles and offers a warranty. Yet, the company is concerned that they may not actually last this long. A test on 25 tires reveals that the mean life of a tire is 39,750 miles, with a standard deviation of 387 miles. Test to see if the tire life is significantly lower than the warranty at α = .01.

• Reject H_o

• Reject H_a

• Fail to reject H_o

• Fail to reject H_a

In performing a hypothesis test where the null

hypothesis is that the μ = 6.9. A random sample of316

items is selected. The sample mean is 7.1 and the sample

standard deviation is 0.6. It can be assumed that the

population is normally distributed at α = .05. You want to test that the true mean is higher than 6.9

• Reject Ho

• Reject Ha

• Fail to reject Ho

• Fail to reject Ha

A P-value indicates:

• the probability that the sample mean is true

• the probability that the alternative hypothesis is true

• the probability of obtaining the results (or one more extreme) if the null hypothesis is true

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

When p-value is greater than alpha we:

• Reject H_o

• Fail to Reject the H_a

• Fail to Reject the H_o

• Reject H_o

Which of the following cannot be an alternative hypothesis?

• μ = 0.5

• μ < 0.5

• μ > 0.5

• μ ≠ 0.5

Given H0: μ = 25, Ha: μ ≠ 25, and P = 0.034. Do you reject or fail to reject H0 at the 0.01 level of significance?

• fail to reject H0

• reject H0

• not sufficient information to decide

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.

Which of the following best describes a Type II error?

• The null is true but we mistakenly reject it.

• The null is false but we mistakenly reject it.

• The null is false but we fail to reject it.

• The null is true but we fail to reject it.