AP Statistics: Ch. 9

Failing to reject a null hypothesis that is false can be characterized as

• 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 it is actually true
• We obtain the wrong test statistic
• We fail to reject the null hypothesis when it's actually false
• We reject the alternate hypothesis when it's actually true

A left-tailed test with n = 41 has a test statistic t = 2.72. Which is the correct p-value?

• 0.0033
• .00486
• .0096
• Not enough
  information

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

Tags

CCSS.HSS.IC.A.1

CCSS.HSS.IC.B.4

A P-value indicates:

• the probability that the null hypothesis 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
• probability of a Type I error

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

• increase
• decrease
• remain the same
• be doubled

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

Tags

CCSS.HSS.IC.B.5

An engineer designs an improved light bulb.  The previous design had an average lifetime of 1200 hours. The new bulb had a lifetime of 1201 hours, using a sample of 2000 bulbs.  Although the difference is quite small, the effect was statistically significant.  The explanation is that

• new designs typically have more variability than standard designs
• the mean of 1200 is large
• the new bulbs last longer than the old bulb
• the sample size is very large

You construct a 95% confidence interval for a mean and find it to be 1.1 ± 0.8. Which of the following is true?

• A test of the hypotheses H₀: μ = 1.2, H_a: μ ≠ 1.2 would reject H₀ at the 0.05 level.
• A test of the hypotheses H₀: μ = 1.1, H_a: μ ≠ 1.1 would reject H₀ at the 0.05 level
• A test of the hypotheses H₀: μ = 0, H_a: μ ≠ 0 would reject H₀ at the 0.05 level
• All three tests above would reject H₀ at the 0.05 level.