Question 1

Assume that we are constructing confidence interval for the difference in the means of two populations based on independent random samples.If both sample sizes  and the distribution 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

False

Question 2

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% confidence level,then we can conclude that we are 95% certain that there is a significant difference between the two population means.

Accepted Answer

The fact that the confidence interval does not include zero (i.e. it is not centered around zero) suggests that there is a significant difference between the two population means. The 95% confidence level means that we are 95% confident that the true difference between the means falls within the interval. Therefore, we can conclude with 95% confidence that there is a significant difference between the two population means.

Question 3

When comparing two population means based on independent random samples,the pooled estimate of the variance is used if both population standard deviations are known.

Accepted Answer

The pooled estimate of the variance is used when the population standard deviations are HYPOTHESIZED to be equal and UNKNOWN. If both population standard deviations are KNOWN, then the variances for each population can be calculated directly and there is no need to use the pooled estimate.

Question 4

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

Accepted Answer

In an independent samples experiment, the samples are chosen randomly and are not related to each other. Therefore, there is no relationship between the measurements in the different samples.

Question 5

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

Accepted Answer

Both assumptions of independent samples and normally distributed populations are required when testing the equality of population variances. Without these assumptions, the test may not be valid.

Question 6

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

Accepted Answer

The answer of When comparing the variances of two normally...

Question 7

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 in order to use a Z statistic.

Accepted Answer

The sample sizes do not need to be equal to use a Z statistic; they just need to be large enough for the Central Limit Theorem to apply, typically n > 30 for each sample.

Question 8

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

Accepted Answer

The alternative hypothesis in this scenario would typically indicate that there is a difference between the two means, so option B is the correct answer.

Question 9

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

Accepted Answer

This statement is false. While a two-sided test is commonly used, it is possible to conduct a one-sided test in certain circumstances. However, it is important to consider the context and reasoning behind choosing a one-sided test, as it may not always be appropriate.

Question 10

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

This is correct. Pooling the proportions assumes that there is no difference between the proportions, consistent with the null hypothesis.

Question 11

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

Accepted Answer

The statement "we are 95% certain that there is a significant difference between the two population means" is incorrect because a confidence interval only provides information about the precision of the sample estimate and not about whether the difference is statistically significant or not. Additionally, the confidence interval includes 0, which suggests that there may not be a significant difference between the means. Therefore, it is not appropriate to conclude that there is a significant difference based solely on the confidence interval.

Question 12

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

Accepted Answer

The Z statistic can be used to test the difference between two means from two independent populations even if the sample sizes are not equal, as long as the populations are approximately normally distributed and the variances are approximately equal.

Question 13

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

Accepted Answer

This is a true statement. When testing the difference between two proportions from populations with large independent samples (typically defined as having at least 10 successes and 10 failures in each sample), the Z test statistic is used.

Question 14

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

Accepted Answer

The degrees of freedom for the t statistic would be calculated as follows: df = (n1-1) + (n2-1) = (13-1) + (10-1) = 21, not 22. Therefore, the statement is false.

Question 15

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

This is true because the F statistic is calculated as the ratio of two variances and can never be negative. Therefore, by definition, its value is always greater than or equal to one.

Question 16

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

Accepted Answer

The answer of In forming a confidence interval for ...

Question 17

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

Accepted Answer

The degrees of freedom for a matched pairs t-test is n - 1, where n is the number of pairs. For 12 pairs, the degrees of freedom would be 11.

Question 18

In testing for the equality of variances from two independent populations,if the null hypothesis is false,the test could result in:
A)A Type I error.
B)Either a Type I error or a Type II error.
C)Neither a Type I error or a Type II error.
D)A Type II error.
E)Both a Type I error and a Type II error.

Accepted Answer

If the null hypothesis is false and the test fails to reject it, it results in a Type II error. This means that the test failed to detect a significant difference in variances when one actually exists in the populations being compared. Therefore, the best choice is D.

Question 19

The F statistic can assume either a positive or a negative value.

Accepted Answer

The F statistic is always non-negative.

Question 20

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 are at least 30.

Accepted Answer

The answer of In testing the difference between the means...

Quiz 10: Statistical Inferences Based on Two Samples