Question 1

How is a pooled estimate of the population proportion represented?

Accepted Answer

The answer of How is a pooled estimate of the...

Question 2

When dependent samples are used to test for differences in the means,we compute paired differences.

Accepted Answer

When dependent samples are used, we compute paired differences by subtracting the corresponding values of one sample from the other. This is done to reduce the effects of individual differences and to focus on the changes within each pair. The paired differences are then used to test for significant differences in the means.

Question 3

In one class,a statistics professor wants to compare grades on the first and second exams.This is an example of paired or dependent observations.

Accepted Answer

The comparison of grades on the first and second exams is an example of paired or dependent observations because the same group of students were taking both exams, and their performance on the first exam can potentially influence their performance on the second exam. Hence, the observations are not independent of each other.

Question 4

For a hypothesis test comparing two population means,the combined degrees of freedom are 24.Which of the following statements about the two sample sizes is NOT true? Assume the population standard deviations are equal.

Accepted Answer

The combined degrees of freedom for two samples with equal variances is calculated as (n1 + n2 - 2). For sample sizes 11 and 13, the degrees of freedom would be 11 + 13 - 2 = 22, not 24.

Question 5

Suppose we test the difference between two proportions at the 0.05 level of significance.If the computed z is -1.07,what is our decision?

Accepted Answer

At the 0.05 level of significance, the critical value for a two-tailed test is ±1.96. Since the computed z of -1.07 is not less than the critical value of -1.96, we fail to reject the null hypothesis. Therefore, our decision is to not reject the null hypothesis.

Question 6

In a market test of a new chocolate raspberry coffee,a poll of 400 people from Dobbs Ferry showed 250 preferred the new coffee.In Irvington,170 out of 350 people preferred the new coffee.To test the hypothesis that there is no difference in preferences between the two villages,what is the alternate hypothesis?

Accepted Answer

The answer of In a market test of a new...

Question 7

When independent samples are used to test for differences in the means,we pool the sample variances.

Accepted Answer

When independent samples are used to test for differences in the means, we assume that the population variances are equal. Therefore, we pool the sample variances to estimate a common variance and use that in our calculations for the test statistic.

Question 8

In a market test of a new chocolate raspberry coffee,a poll of 400 people (sample 1)from Dobbs Ferry showed 250 preferred the new coffee.In Irvington,170 (sample 2)out of 350 people preferred the new coffee.To test the hypothesis that a higher proportion of people in Dobbs Ferry prefer the new coffee,what is the alternate hypothesis?

Accepted Answer

The alternate hypothesis should state that the proportion of people who prefer the new coffee in Dobbs Ferry is higher than the proportion in Irvington. Based on the given data, it can be stated as:
B: The proportion of people in Dobbs Ferry who prefer the new coffee is greater than the proportion of people in Irvington who prefer the new coffee.

Question 9

For a hypothesis comparing two population means,what is the critical value for a one-tailed hypothesis test,using a 5% level of significance level,with both sample sizes equal to 13? Assume the population standard deviations are equal.

Accepted Answer

The answer of For a hypothesis comparing two population means,what...

Question 10

When dependent samples are used to test for differences in the means,we pool the sample variances.

Accepted Answer

When dependent samples are used to test for differences in the means, we do not pool the sample variances. Instead, we calculate the differences between each pair of paired observations and use those differences to calculate the mean difference and standard deviation of the differences. These values are then used in a t-test to test for a significant difference in the means. Pooling the variances would potentially lead to an inflated standard error of the mean difference and an incorrect hypothesis test result.

Question 11

The net weights (in grams)of a sample of bottles filled by a machine manufactured by Edne,and the net weights of a sample filled by a similar machine manufactured by Orno,Inc. ,are: Edne: 5,8,7,6,9 and 7
Orno: 8,10,7,11,9,12,14 and 9
Testing the claim at the 0.05 level that the mean weight of the bottles filled by the Orno machine is greater than the mean weight of the bottles filled by the Edne machine,what is the critical value? Assume equal standard deviations for both samples.

Accepted Answer

The answer of The net weights (in grams)of a sample...

Question 12

If two dependent samples of size 20 are used to test the difference between the means,the degrees of freedom for a t-statistic is 19.

Accepted Answer

The degrees of freedom for a t-test comparing two dependent samples is calculated as n - 1, where n is the sample size. For a sample size of 20, the degrees of freedom would be 20 - 1 = 19.

Question 13

Which of the following conditions must be met to conduct a test for the difference in two sample means?

Accepted Answer

To conduct a test for the difference in two sample means, data must be at least of interval scale and populations must be normal. The assumption of equal variances can also be made, but there are methods to account for unequal variances. Therefore, A and B are correct.

Question 14

If the null hypothesis that two means are equal is true,where will 97% of the computed z-values lie between?

Accepted Answer

The answer of If the null hypothesis that two means...

Question 15

If two independent samples of size 10 are used to test the difference between the means,the degrees of freedom for a t-statistic are 18.

Accepted Answer

The degrees of freedom for a t-test comparing two independent samples of size 10 would be 18 only if the pooled variance estimate is used. However, it is not specified in the given statement whether the pooled variance estimate is used or not. Therefore, we cannot determine the degrees of freedom for the t-test from the given information, and the statement is false.

Question 16

If the decision is to reject the null hypothesis of no difference between two population proportions at the 5% level of significance,what are the alternate hypothesis and rejection region?

Accepted Answer

The answer of If the decision is to reject the...

Question 17

Administering the same test to a group of 15 students and a second group of 15 students to see which group scores higher is an example of

Accepted Answer

A two sample test of means compares the means of two independent groups. In this case, we are comparing the test scores of two separate groups of students. A one sample test of means would be used to compare the mean of one group to a known population mean. A paired t-test would be used when comparing two related groups (e.g. the same group of students before and after an intervention). A test of proportions would be used when comparing the proportions of two groups instead of the means.

Question 18

Using two independent samples,we test for a hypothesized difference between two population means.The population standard deviations are equal.The number in the first sample is fifteen and the number in the second sample is twelve.How many degrees of freedom are associated with the critical value?

Accepted Answer

The answer of Using two independent samples,we test for a...

Question 19

When is it appropriate to use the paired difference t-test?

Accepted Answer

The paired difference t-test is used when comparing two dependent samples, such as before and after measurements or matched pairs. It is not appropriate for comparing more than two samples at once or two independent samples. Therefore, option D is the best choice as it correctly identifies the appropriate scenario for using the paired difference t-test.

Question 20

For a hypothesis comparing two population means,what is the critical value for a one-tailed hypothesis test,using a 5% level of significance level,with both sample sizes equal to 13? The standard deviations for the samples are 5 and 7.Assume the population standard deviations are unequal.

Accepted Answer