AP Stat Inference

To assess the accuracy of a kitchen scale, a standard weight, known to weigh 1.000 gram, is weighed a total of n times, and the mean of the n weight measurements is computed. (If a 90% confidence interval for the mean calculated from these measurements does not contain 1.000, the scale is deemed inaccurate.) Suppose the scale readings are Normally distributed and that similar scales are known to measure such weights with a standard deviation of σ = 0.01 gram. Which of the following is the smallest value of n that will produce a 90% confidence interval with a margin of error of at most 0.001 grams?

• 17

• 271

• 385

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

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 researcher plans to conduct a test of hypotheses at the a = 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 II error for the particular alternative value of the parameter at which she computed the power is

• 0.01

• 0.10

• 0.89

• 0.90

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 or this test?

• larger than 0.1

• between 0.1 and 0.05

• between 0.05 and 0.01

• below 0.01

Many people believe that playing chess can have a positive effect on reading ability. A sample of n = 53 students was chosen. They participated in a comprehensive chess program, after which they were given a reading test. What is the correct t* for a 90% confidence interval for the true mean reading score?

• 1.645

• 1.671

• 1.676

• 2.009

Find the P-Value for a right-tailed test with a test statistic of t = 1.6 and n = 20

• .0630

• .9370

• .9452

• .0548

• A
• B
• C
• D