Exam 10: A: Inference From Small Samples

A test is being conducted to test the difference between two population means using data that are gathered from a matched pairs experiment. If the paired differences are normal, then which distribution should be used for testing?

Two random samples of sizes 25 and 20 are independently drawn from two normal populations, where the unknown population variances are assumed to be equal. The number of degrees of freedom of the equal-variances t-test statistic is 44.

Two samples of sizes 15 and 20 are randomly and independently selected from two normally distributed populations, where the unknown population variances are assumed to be equal. The number of degrees of freedom associated with the two-sample t test is equal to 35.

Which one of the following conditions is assumed with the t test for the difference between the means of two independent populations?

A major department store chain is interested in estimating the average amount its credit card customers spent. Fifteen credit card accounts were randomly sampled and analyzed with the following results: = $50.50 and = 400. Which of the following is a 95% confidence interval for the average amount the credit card customers spent?

Which of the following is NOT a required assumption for constructing a confidence interval estimate of the difference between two population means when the samples are small?

When the population variances are unequal, we estimate each population variance with its sample variance. Hence, the unequal-variances test statistic of is Student's t distributed with + - 2 degrees of freedom.

In order to determine the p-value associated with hypothesis testing about the population mean , it is necessary to know the value of the test statistic.

A Canadian Forces drill instructor recorded the time in which each of 15 recruits completed an obstacle course both before and after basic training. To test whether any improvement occurred, the instructor would use a t distribution with 15 degrees of freedom.

The Student's t distribution is a sampling distribution for a random variable, t, derived from a normally distributed population, that is (1) single-peaked above the random variable's mean, median, and mode of 0; (2) perfectly symmetrical about this central value; and (3) characterized by tails extending indefinitely in both directions from the centre, approaching, but never touching, the horizontal axis.

If a sample has 18 observations and a 90% confidence estimate for is needed, the appropriate t score is 1.740.

When small samples are used to estimate the true population mean where the population standard deviation is unknown, the t distribution must be used to obtain the critical value.

The value of F that locates an area 0.01 in the upper tail of the F distribution for = 15 and = 10 is 3.80.

Matched pairs sampling is a procedure that matches each unit from population A with a "twin" from population B so that any sample observation about a unit in population A automatically yields an associated observation about a unit in population B.

Which of the following is a characteristic of the chi-square distribution?

The "shape" of the t distribution changes as the value of the sample mean changes.

Regardless of the degrees of freedom, every t distribution is symmetric around 0.

Given the information: , , , , how many degrees of freedom should be used in the pooled variance t test?

Under which of the following circumstances is it impossible to construct a confidence interval for the population mean?

Matched pairs sampling is designed to control for extraneous factors that might influence the characteristic being measured in addition to the variable under study.