AP Stats Inferences for Means

What is the t value associated with 90% confidence and a sample size of 15?

• 1.341
• 1.345
• 1.761
• 1.753

Which z-value is used for a 95% confidence interval?

• 1.65
• 1.96
• 2.58
• 2.33

Construct a 95% confidence interval for the population mean, mu.  Assume the population has a normal distribution.  A sample of 25 randomly selected students has a mean test score of 81.5 with a sample standard deviation of 10.2

• (77.3, 85.7)
• (87.1, 98.3)
• (66.4, 69.9)
• (77.5, 85.5)

You are thinking of using a t procedure to construct a 95% confidence interval for the unknown mean μ of a population for a random sample taken from the population. You suspect that the distribution of the population is not Normal and may in fact be moderately skewed. Which of the following statements is then correct?

• You should not use the t procedure, since the population does not have a Normal distribution.
• You can use the t procedure provided that n>30 .
• You can use the t procedure regardless of the sample size since t procedures are robust against non-Normality.

Which of the following changes to a study would result in a narrower confidence interval?

• increasing the confidence level, increasing the sample size
• decreasing the confidence level, decreasing the sample size
• increasing the confidence level, decreasing the sample size
• decreasing the confidence level, increasing the sample size.

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 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

Which of the following 95% confidence intervals would lead us to reject H₀: p = 0.30 in favor of H_a: p ≠ 0.30 at the 5% significance level?

• (0.19, 0.27)

• (0.27, 0.31)

• (0.24, 0.30)

• (0.29, 0.38)

A student’s AP statistics project involves comparing the time it takes a student to complete a set of 25 basic trinomial factoring problems while listening to either rap music or country music. Twelve students are timed on two different sets of problems and the order of both which set of problems he does first and which music he listens to first are randomized. The resulting data is thus paired, with each student acting as his own “pair.” Which of the following conditions is required to perform a t-test on these paired data?

• The distribution of times for all students on each set of problems must be approximately Normal.

• The distribution of times for all students while listening to each type of music must be approximately Normal.

• The distribution of times for all 24 sets of problems (12 students are taking 2 tests each) must be approximately Normal.

• The distribution of differences between each individual student’s times on each of the two tests (time with rap – time with country) must be approximately Normal.

An SRS of 100 postal employees found that the average time these employees had worked for the postal service was J = 7 years with standard deviation s = 2 years. Assume the distribution of the time the population of employees have worked for the postal service is approximately Normal with mean m. Are these data evidence that m has changed from the value of 7.5 years of 20 years ago? To make this determination we test the hypotheses H0: m = 7.5, Ha: m 7.5 using a one-sample t test. Which of the following intervals contains the P-value for this test?

• larger than 0.1

• between 0.1 and 0.05

• between 0.05 and 0.01

• below 0.01