Chapter 7: Hypothesis Testing

The chi-square distribution is used for inferences about the mean when σ is not known.

• True

• False

A car manufacturer advertises that its new subcompact models get 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 = 47
  H_a = 47
• H₀ = 47
  H_a < 47
• H₀ = 47
  H_a > 47
• H₀ = 47
  H_a ≠ 47

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

Choose the pair that provide a legitimate hypothesis.

• H_o: p≠.4, H_a: p>.4

• H_o:p̂=.16, H_a: p̂>.16

• H_o:μ=24, H_a:μ≠24

In a random sample of 1000 adult Americans, only 430 could name at least one justice who is currently serving on the US Supreme Court. A claim is that fewer than half of adult Americans can name at least one justice who is currently serving on the US Supreme Court. State the alternative hypothesis.

• H_a: p=.5, where p is the true proportion of Americans who can name one justice currently serving.

• H_a: p>.5, where p is the true proportion of Americans who can name one justice currently serving.

• H_a: p<.5, where p is the true proportion of Americans who can name one justice currently serving.

In a national survey of 2013 adults, 1283 indicated that they believe rudeness is a more serious problem than in years past.  Does this indicate that more than 3/4 of American adults believe rudeness is a worsening problem? State the alternative hypothesis.

• H_a: p > .75, where p is the true proportion of Americans who believe rudeness is worsening.
• H_a: p = .75, where p is the true proportion of Americans who believe rudeness is worsening.
• H_a: p <.75, where p is the true proportion of Americans who believe rudeness is worsening.

What is the critical value, z_o,  for a left-tailed test with α = 0.05. 

• z₀ = -1.645
• z₀ = -2.33
• z₀ = -1.96
• z₀ = 2.58

What is the critical value, z_o, for a right-tailed test with α = 0.01. 

• z₀ = -1.645
• z₀ = 2.33
• z₀ = -1.96
• z₀ = 2.58

Given the following information, find the standardized test statistic for the sample.

x-bar = 68, μ = 71, σ = 7.5, n = 36

• -2.40

• -3.00

• 2.40

• 66.44

Given the following scenario, state whether we would fail to reject or reject the null. 

• Reject H₀
• Fail to reject H₀

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