Exam 10: A: Inference From Small Samples

To test the difference between two population means by applying the two-sample procedure that uses a pooled estimate of the common variance , the two samples must be independent of each other.

When testing for the difference between two population variances with sample sizes of and , what are the numbers of degrees of freedom?

The exact shape of the F distribution is determined by two numbers of degrees of freedom.

The equal-variances test statistic of is Student's t distributed with + degrees of freedom, provided that the two populations are normal.

When comparing two population means using data that are gathered from a matched pairs experiment, the test statistic for is Student's t distributed, with degrees of freedom, provided that the differences are normally distributed.

The 90th percentile of a chi-square distribution with 15 degrees of freedom is equal to 22.3072.

What is the term used to describe samples in which there exists some natural relationship between each pair of observations that provides a logical reason to compare the first observation of sample 1 with the first observation of sample 2, the second observation of sample 1 with the second observation of sample 2, and so on?

A random sample of size 10 produced a sample mean equal to 12 and a standard deviation equal to 0.15. Based on this information, the margin of error associated with a 90% confidence interval estimate for the population mean is 1.8331.

Two random samples of 10 and 12 observations produced sample variances equal to 7.50 and 3.20, respectively. Which of the following is the calculated value of the test statistic when testing vs. ?

In testing whether the means of two normal populations are equal, summary statistics computed for two independent samples are as follows: , , , , , and . Assume that the population variances are equal. What is the standard error of the sampling distribution of the sample mean difference ?

In testing the difference between two population means using two independent samples, when is the sampling distribution of the sample mean difference normal?

For which of the following ratios is its sampling distribution the F distribution ?

A 90% confidence interval estimate for the population mean constructed with a small sample will have a margin of error that is approximately 90% of the population size n.

In testing for differences between the means of two matched pairs populations, how may the null hypothesis best be formulated?

A Canadian Forces instructor recorded the time in which each of 10 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 nine degrees of freedom.

Which of the following is NOT a property of the F distribution?

Researchers determine that 60 tissues is the average number of tissues used during a cold. Suppose a random sample of 100 users yielded the following statistics on the number of tissues used during a cold: = 52 and s = 22. Using the sample information provided, what is the value of the test statistic?

The matched pairs experiment always produces a larger test statistic than the independent-samples experiment.

The area under a chi-square curve with 10 degrees of freedom, which is captured between the critical values , is .

For which kinds of data can we design a matched pairs experiment? Choose the best response.