AP Statistics Intro to Hypothesis Testing

Failing to reject a null hypothesis when you should have is called:

• a Type I error

• a Type II error

• both a Type I and Type II error

• no error

A Type I error is when:

• We reject the null hypothesis when we should not have

• We reject the null hypothesis when we should have accepted it

• We fail to reject the null hypothesis when it's actually false

• We reject the alternate hypothesis when it's actually true

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 suspect that the advertised mpg is an over estimate of the truth?

• H₀: µ = 47

  H_a: µ = 47

• H₀: µ = 47

  H_a: µ < 47

• H₀: µ = 47

  H_a: µ > 47

• H₀: µ = 47

  H_a: µ ≠ 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?

• H₀: μ=21

  H_a: μ<21

• H₀: p=.20

  H_a: p<.20

• H₀: p< .21

  H_a: p= .21

• H₀: p= .21

  H_a: p< .21

A P-value indicates:

• the probability that the null hypothesis is true

• the probability that the alternative hypothesis is true

• the probability of obtaining a result as extreme or more extreme than the one we obtained

• probability of a Type I error

A hypothesis test tests the null hypothesis H₀: μ = 20 against the alternative hypothesis H_a: μ ≠ 20 at a significance level of alpha. If the same procedure is used to test H₀: μ = 20 against H_a: μ > 20 with the same data then the p-value will

• increase

• decrease

• remain the same

• be doubled

How do you calculate the degrees of freedom for a t-procedure?

• It is equal to the p-value.

• It is equal to 1 – (p-value).

• It is equal to the significance level.

• It is equal to n-1

In testing hypotheses, which of the following would be strong evidence against the null hypothesis?

• using a small level of significance
• using a large level of significance
• obtaining data with a small p-value
• obtaining data with a low test statistic

A researcher plans to conduct a test of hypotheses at the α = 0.01 significance level. She designs her study to have a power of 0.90 at a particular alternative value of the parameter of interest. The probability that the researcher will commit a Type I error is

• 0.01

• 0.10

• 0.90

• 0.99

In a test of H₀: p = 0.3 against H_a: p ≠ 0.3, a sample of size 65 produces 28 successes. Which of the following is closest to the P-Value of the test?

• 0.0054

• 0.0107

• 0.0214

• 0.4308