AP Statistics Inference Tests and Intervals

I31: The number of 911 calls per day in a small Midwestern town is noted for a sample of 60 days with x̄ = 23.4 and s = 3.7. With what degree of confidence can we assert that the mean number of 911 calls per day in this town is between 22.4 and 24.4?

• 48%

• 90%

• 95%

• 96%

• 99%

Suppose (48, 65) is a 95% confidence interval estimate for a population mean μ. Which of the following is a true statement?

• There is a 0.95 probability that μ is between 48 and 65.

• If 100 random samples of the given size are picked and a 95% confidence interval estimate is calculated from each, then μ will be in 95 of the resulting intervals.

• If 95% confidence intervals are calculated from all possible samples of the given size, μ will be in 95% of these intervals.

• The probability that μ is in any particular confidence interval can be any value between 0 and 1.

• Confidence level cannot be interpreted until after data is obtained.

In a random survey of 450 adults, 28% said that they felt that their credit card debt is too high. With what degree of confidence can the pollster say that 28 ± 4 percent of adults believe that their credit card debt is too high?

• 70%

• 91%

• 94.1%

• 95%

• 96%

When an online news magazine asked viewers to click their agreement or disagreement, 300 out of 1,200 respondents agreed with a statement that the most practical way of becoming a millionaire is winning a lottery. Immediate feedback stated that 25% of the viewers, with a margin of error of ± 2.5%, agreed with the statement. Fine print claimed 95% confidence. What is the proper conclusion?

• We are 95% confident that the proportion of viewers who believe that the most practical way of becoming a millionaire is winning a lottery is between 0.225 and 0.275.

• Without knowing whether both np and n(1-p) are > 10, the calculation is inappropriate.

• Without knowing whether or not the 1,200 respondents are 10% of all viewers, the calculation is inappropriate.

• The z-distribution was inappropriately used instead of the t-distribution.

• The data was not an SRS, so the calculation is inappropriate.

2000 children were surveyed and the report that followed said, "With 98% confidence, between 20% and 50% of all parents make their children eat breakfast." What does 98% confidence mean in this situation?

• We can be 98% confident that the method used to get the intervals always gives the correct answer

• 98% of all parents will make their kids eat breakfast

• When used repeatedly, the method used to find the interval produces intervals which include the true proportion about 98% of the time

• The kids were 98% confident that they ate breakfast that day.

Which of the following would not decrease the width of a confidence interval?

• I only

• II only

• III only

• I and II only

• II and III only

• A

• B

• C

• D

• E

Place the descriptors next to the intervals

c

d

Same Sample Size

Smaller Sample Size

Larger Sample Mean

Smaller Sample Mean

Larger Sample Size

Same Sample Size

These symbols represent the mean and standard deviation for which of the following distributions?

• The Population

• The Sample

• The Sampling Distribution

Given the same mean, SD, and sample size, a confidence interval of 80% would be wider than a confidence interval of 90%

• True

• False