Question 1

In an experiment involving matched pairs, a sample of 12 pairs of observations is collected. The degrees of freedom for the t statistic is 10.

Accepted Answer

Degrees of freedom is n − 1 = 12 − 1 = 11

Question 2

In testing the difference between two population variances, it is a common practice to compute the F statistic so that its value is always greater than or equal to one.

Accepted Answer

The F statistic is the ratio of two quantities, in this case, variances that are expected to roughly be equal to 1 under the null hypothesis.

Question 3

There are two types of machines, called type A and type B. Both type A and type B can be used to produce a certain product. The production manager wants to compare efficiency of the two machines. He assigns each of the 15 workers to both types of machines to compare their hourly production rate. In other words, each worker operates machine A and machine B for one hour each. These two samples are independent.

Accepted Answer

This is a paired sample because both machines have the same operators.

Question 4

In testing the difference between the means of two normally distributed populations using large independent random samples, the sample sizes from the two populations must be equal.

Accepted Answer

Sample sizes do not have to be equal to test the differences of the means.

Question 5

In testing the difference between two means from two independent populations, the sample sizes do not have to be equal.

Accepted Answer

Each sample size needs to be large.

Question 6

If the limits of the confidence interval of the difference between the means of two normally distributed populations were from −2.6 to 1.4 at the 95 percent confidence level, then we can conclude that we are 95 percent certain that there is a significant difference between the two population means.

Accepted Answer

Because zero is in the interval, we cannot assume that there is a significant difference between the two means at the 95 percent confidence level.

Question 7

The controller of a chain of toy stores is interested in determining whether there is any difference in the weekly sales of store 1 and store 2. The weekly sales are normally distributed. This problem should be analyzed using an independent means method.

Accepted Answer

These stores are independent and there is no relationship between the two stores.

Question 8

In forming a confidence interval for μ₁ − μ₂, only two assumptions are required: independent samples and sample sizes of at least 30.

Accepted Answer

The assumptions are independent samples, equal variances, and either sample sizes are large or the sampled populations are normally distributed.

Question 9

In testing the equality of population variances, two assumptions are required: independent samples and normally distributed populations.

Accepted Answer

The samples need to come from normally distributed populations and then these two samples need to be independent. They cannot have a relationship between them.

Question 10

When testing the difference between two proportions selected from populations with large independent samples, the z test statistic is used.

Accepted Answer

This is because we can estimate the standard deviation via the two proportions.

Question 11

When comparing two population means based on independent random samples, the pooled estimate of the variance is used when there is an assumption of equal population variances.

Accepted Answer

This is because we are assuming that all of the standard deviations are equal.

Question 12

Assume that we are constructing a confidence interval for the difference in the means of two populations based on independent random samples. If both sample sizes n₁ and n₂ =10, and the distributions of both populations are highly skewed, then a confidence interval for the difference in the means can be constructed using the t test statistic.

Accepted Answer

With small sample sizes and skewed populations, we should use a nonparametric test, not a t test statistic.

Question 13

If the limits of the confidence interval of the difference between the means of two normally distributed populations were 8.5 and 11.5 at the 95 percent confidence level, then we can conclude that we are 95 percent certain that there is a significant difference between the two population means.

Accepted Answer

This is true because the confidence interval does not contain 0.

Question 14

When comparing the variances of two normally distributed populations using independent random samples, if s₁² = s₁², the calculated value of F will always be equal to one.

Accepted Answer

An F test is roughly equal to 1 under the null hypothesis.

Question 15

When we are testing a hypothesis about the difference in two population proportions based on large independent samples, we compute a combined (pooled) proportion from the two samples if we assume that there is no difference between the two proportions in our null hypothesis.

Accepted Answer

We would not use this pooled estimate if the hypothesized difference were nonzero.

Question 16

In testing the difference between the means of two normally distributed populations using independent random samples, the alternative hypothesis always indicates no difference between the two specified means.

Accepted Answer

The alternative hypothesis can be a difference or greater than or less than.

Question 17

When comparing two independent population means, if n₁ = 13 and n₂ = 10, degrees of freedom for the t statistic is 22.

Accepted Answer

Degrees of freedom = n₁ + n₂ − 2 = 13 + 10 − 2 = 21

Question 18

In testing the difference between the means of two normally distributed populations using independent random samples, we can only use a two-sided test.

Accepted Answer

Using the critical value rules, we should use a two-sided test if the test is of no differences between the two samples. If we are looking at a greater than or less than difference, we would use a one-sided test.

Question 19

In testing the difference between the means of two independent populations, if neither population is normally distributed, then the sampling distribution of the difference in means will be approximately normal, provided that the sum of the sample sizes obtained from the two populations is at least 30.

Accepted Answer

We need each sample to be large (at least greater than 30).

Question 20

An independent samples experiment is an experiment in which there is no relationship between the measurements in the different samples.

Accepted Answer

Different samples from the first population would give different values of the mean, and different samples from the second population would give different values of the mean.

Quiz 11: Statistical Inferences Based on Two Samples