AP Stats Unit 6

We are trying to estimate the difference between the SAT scores of students who have taken AP Statistics, and students who have not taken AP Statsitics. We calculate a 90% confidence interval, and get (50, 120). Interpret the confidence interval in context.

• We are 90% confident that AP Stats students score a 120 on the SAT, but non-AP Stats students score a 50 on the SAT

• 90% of the time, we will get a confidence interval between 50 and 120.

• We are 90% confident that the SAT scores of students that have taken AP Stats are between 50 and 120 points higher than the SAT scores of students that have not taken AP Stats.

• 90% of the students that have taken AP Stats score between 50 and 120 points higher than students that have not taken AP Stats.

A certain population follows a normal distribution with mean μ and standard deviation σ. You construct a 95% confidence interval for μ and find it to be 1.1 ± 0.9. Which of the following is true?

• In a test of the hypotheses Ho: μ=1.2, HA: μ≠1.2, HO would be rejected at the .05 level.

• In a test of the hypotheses Ho: μ=1.9, HA: μ≠1.9, HO would be rejected at the .05 level.

• In a test of the hypotheses Ho: μ=1.9, HA: μ≠1.9, HO would be rejected at the .025 level.

• In a test of the hypotheses Ho: μ=0, HA: μ≠0, HO would be rejected at the .05 level.

• A conclusion about hypotheses cannot be made from a confidence interval.

A company claims its program will allow your computer to download movies quickly. We’ll test the free evaluation copy by downloading a movie several times, hoping to estimate the mean download time with a margin of error of only 8 minutes. We think the standard deviation of download times is about 10 minutes. Which of the following sample sizes would guarantee a margin of error of less than 8 minutes if we want to be 95% confident?

• 6

• 10

• 11

• 15

• None of these

You perform a hypothesis test with H0: mu=12, HA: mu>12

Suppose that HA is true. For a fixed sample size and significance level α, the power of the test will be greatest if the actual mean is which of the following?

• mu=3

• mu=13

• mu=13.5

• mu=16

Which of the following is a condition for choosing a t-interval rather than a z-interval when constructing a confidence interval for the mean of a population?

• The standard deviation of the population is unknown.

• There is an outlier in the sample data.

• The sample may not have been a simple random sample.

• The population is not normally distributed.

• The data are linked so a matched-pairs test is necessary.

A two-sided hypothesis test for a population mean is significant at the 1% level of significance. Which of the following is necessarily true?

• The 99% confidence interval of the mean contains 0.

• The 99% confidence interval of the mean does not contain 0.

• The 99% confidence interval of the mean contains the hypothesized mean.

• The 99% confidence interval of the mean does not contain the hypothesized

  mean.

• The 99% confidence interval is not useful here.

Which of the following is not a characteristic of the t-distribution

• It is unimodal

• It is symmetric

• It is bell-shaped

• It gets wider with increasing degrees of freedom

• It approaches the normal distribution as the degrees of freedom increase

A one sample t test yields a t statistic of 2.089. The sample size was 16. The alternative hypothesis was in the form Ha : μ > 37. Is there significant evidence at the α = .05 level to reject the null hypothesis?

• No, because the P-value is between 0.05 and 0.10.

• No, because the P-value is between 0.025 and 0.05.

• No, because the sample mean was significantly above 37.5.

• Yes, because the P-value is between 0.05 and 0.10.

• Yes, because the P-value is between 0.025 and 0.05.

We calculate a confidence interval for the difference of means, and get (15, 19). Which of the following best represents the point estimate, and the margin of error?

• x-bar1-x-bar2=17, MOE=2

• mu1-mu2=15, MOE=4

• p-hat1-p-hat2=15, MOE=4

• p1-p2=17, MOE =4

We run a hypothesis test for to find out the difference between the proportion of AP Stats students and non-AP Stats students that major in a STEM field after graduating high school. Our hypotheses are H0: p1-p2=0 and HA: p1-p2>0, where p1 is the proportion of AP Stats students that major in STEM, and p2 is the proportion of AP Stats students that don't major in STEM. We get a p-value of 0.01. Interpret this p-value in context.

• There is a 0.01 chance of getting the exact result we did.

• There is a 0.01 chance of getting our sample result, or one more extreme, if there is actually no difference in the proportion of students that major in STEM.

• There is a 0.01 chance that we are correct in rejecting the null-hypothesis

• 1% of the samples we could have taken would have had the exact same difference of proportions that our sample did.