Quiz R 7(2), 8

A population has a non-normal distribution with mean μ and variance σ2. The sampling distribution of the sample mean computed from samples of large size from that population will have

• the same distribution as the population distribution
• its mean approximately equal to the population mean
• its variance approximately equal to the population variance

A survey is taken to determine whether the average starting salaries of CFA charterholders is equal to or greater than $54,000 per year. Assuming a normal distribution, what is the test statistic given a sample of 75 newly acquired CFA charterholders with a mean starting salary of $57,000 and a standard deviation of $1,300?

• -19.99
• 19.99
• 2.31

For a two-tailed test of hypothesis involving a z-distributed test statistic and a 5% level of significance, a calculated z-statistic of 1.5 indicates that

• the null hypothesis cannot be rejected
• the test is inconclusive
• the null hypothesis is rejected

A researcher is testing whether the average age of employees in a large firm is statistically different from 35 years (either above or below). A sample is drawn of 250 employees and the researcher determines that the appropriate critical value for the test statistic is 1.96. The value of the computed test statistic is 4.35. Given this information, which of the following statements is least accurate? The test

• indicates that the researcher will reject the null hypothesis
• has a significance level of 95%

• indicates that the researcher is 95% conídent that the average employee age is diìerent than 35 years

Which of the following statements about hypothesis testing is most accurate? A Type II error is the probability of

• failing to reject a false null hypothesis
• rejecting a true alternative hypothesis
• rejecting a true null hypothesis

Ron Jacobi, manager with the Toulee Department of Natural Resources, is responsible for setting catch-and-release limits for Lake Norby, a large and popular fishing lake. He takes a sample to determine whether the mean length of Northern Pike in the lake exceeds 18 inches. If the sample t-statistic indicates that the mean length of the fish is significantly greater than 18 inches, when the population mean is actually 17.8 inches, the t-test resulted in:

• both a Type I and a Type II error
• a Type II error only
• a Type I error only

A financial analyst is constructing a hypothesis test to assess whether the mean daily return on a portfolio of blue-chip stocks is statistically different from zero. The sample size is 128 trading days, the mean return is 0.14%, and the standard deviation is 0.18%. With the null hypothesis that the daily portfolio return is equal to zero, which of the following changes in variables will independently make it more likely that the null is rejected?

• An increase in the standard deviation of the returns to 0.23%
• A move of the mean return down to 0.11%
• An increase in the sample size to 140

When evaluating mean differences between two dependent samples, the most appropriate test is a

• z-test
• chi-square test
• paired comparisons test

A chi-square test is most appropriate for tests concerning

• a single variance
• differences between two population means with variances assumed to be equal
• differences between two population means with variances not assumed to be equal

Which of the following tests should be used to test the difference between the variances of two normally distributed populations with random independent samples

• t-test
• F-test
• Paired comparisons test