Statistics Confidence Intervals and Significance Test

Jimmy is interested in comparing the fitness level of the members of his gym to the levels at a competing gym. He randomly selected 125 members of his gym and found 75 passed a fitness test. 70 of 95 at the other gym passed. Which interval estimates, with 96% confidence, the difference in proportion of members in Jimmy's gym who can pass the test and the proportion from the other gym who can pass?

• (-0.2404, -0.033)

• (-0.2602, -0.0135)

• (-0.2661, -0.0076)

• (-0.3490, -0.1099)

• (-0.3547, -0.1042)

A restaurant manager will randomly select a sample of filled cups each day and measure the volume of liquid in each cup. Past measurements have shown that the standard deviation of liquid dispensed by this machine is 0.2 ounces. An estimate of the mean volume must be reported within a margin of error of 0.1 ounces with 98% confidence. What is the minimum sample size for the number of drinks the manager must select?

• 2

• 5

• 16

• 17

• 22

A nutritionist claims U.S. children drink an average of less than 2 glasses of milk per day. Based on an SRS of 30 children, the p-value of H₀: μ = 2 vs. H_A: μ < 2 is 0.0015. What is the correct interpretation of the p-value?

• The probability that she fails to reject the null hypothesis is 0.015%

• The probability that she rejects the null is 0.015%

• She can be 99.85% confident that the alternative hypothesis is true

• About 0.15% of all samples would product a test statistics at least as extreme as ours if the null hypothesis is true.

• About 99.85% of all samples would product a test statistics at least as extreme as ours if the null hypothesis is true.

The process of making cough drops yields drops with varying amounts of the active ingredient. It is claimed that the average amount of this ingredient per tablet is at least 400mg. We test a random sample of 90 tablets. The mean content of the active ingredient for the sample is 396.8mg, while the standard deviation is 31mg. What is the approximate p-value for the appropriate test?

• 0.050

• 0.100

• 0.165

• 0.330

• 0.335

A major department store wants to compare the mean number of customers an employee can process per hour using two new scanning systems. 100 employees are randomly selected and then randomly assigned to one of the new systems. After each group of 50 has been trained on one scanning system and 50 on the other, the number of customers processed per hour is recorded. Which test is most appropriate for this situation?

• 1-sample t-test

• 2-sample t-test

• Paired t-test

• 1-sample z-test

• 2-sample z-test

Which of the following statements is/are true about a t-distribution with k degrees of freedom?

• I only

• II only

• I and II only

• II and III only

• I, II, and III

Which of the following is not a condition that needs to be checked for inference for proportions?

• Ensuring that the sample is independent

• Making sure the sample is representative of the population

• n*p₀ > 10, n*q₀ > 10

• n*p-hat > 10, n*q-hat > 10

z* is the critical value for which of the following tests/intervals?

I. 1-prop. z-test

II. 2-prop. z-interval

III. 1-sample t-test

IV. 2-sample t-interval

• I only

• I and II only

• I, II, and III only

• All of the above

• III and IV only

A rubber band man claims that p, the proportion of bands that snap when stretched beyond 8 inches, is no more than 0.03. Some customers have complained that this happens more frequently. Which of the following sets of hypotheses would the customers used to conduct an experiment to test the rubber band man's claim?

• H₀: p ≠ 0.03, H_A: p = 0.03

• H₀: p = 0.03, H_A: p > 0.03

• H₀: p = 0.03, H_A: p ≠ 0.03

• H₀: p = 0.03, H_A: p < 0.03

• H₀: p > 0.03, H_A: p = 0.03

An appropriate 95% confidence interval for μ has been calculated as ( − 0.73, 1.92) based on n = 15 observations from a population with a Normal distribution. If we wish to use this confidence interval to test the hypothesis Ho: μ = 0 against Ha: μ ≠0, which of the following is a legitimate conclusion?

• Reject Ho at the

  α = 0.05 level of significance.

• Fail to reject Ho at the α = 0.05 level of significance.

• Reject Ho at the

  α = 0.10 level of significance.

• Fail to Reject Ho at the α = 0.10 level of significance.