Ch 8. Hypothesis Testing with Two Samples

Using Appendix B in your text to assist you,, what would be the appropriate critical at the .05 level of significance, given the following test situation: Test based upon two independent samples; 11 cases in one sample and 19 cases in the other.

2.048

Using Appendix B in your text to assist you, what would be the appropriate critical at the .05 level of significance, given the following test situation: Test based upon two matched or related samples; 22 cases with 22 pre-test scores and 22 post-test scores.

2.080

Assume two independent samples and the following information: Mean of group 1 (X1) = 53.92 Sample size of group 1 (n1) = 11 Mean of groups 2 (X2) = 50.0 Sample size of group 2 (n2) = 17 Estimated standard error of the differene b/t means (Sx1 - x2) = 2.80 Calculate t. Assuming a .05 level of significance (α = .05), do you reject or fail to reject the null hypothesis?

Calculated test statistic: t = 2.056 Critical value: t = 1.40 Fail to reject the null hypothesis.

Assume that you have conducted a t test with matched samples. Your test is based upon the before and after scores of 15 research participants, and you have selected the .05 level of significance. You have calculated your test statistic and it is equal to 2.010. Using Appendix B to allow you to find the appropriate critical value, which of the following would be the proper interpretation of your results?

Fail to reject the null hypothesis

The t test for independent samples:

requires interval/ratio data and two samples which can have an unequal number of cases

Assume that you have conducted a t test with independent samples, and you are using the .01 level of significance. One sample involves 10 cases and the other sample involves 12 cases. You have calculated your test statistic; it is equal to 2.915. Using Appendix B to allow you to find the appropriate critical value, which of the following would be the proper interpretation of your results?

Reject the null hypothesis

Assume that you have conducted a t test with independent samples, and you are using the .05 level of significance. One sample involves 16 cases and the other sample involves 13 cases. You have calculated your test statistic; it is equal to 2.311. Using Appendix B to allow you to find the appropriate critical value, which of the following would be the proper interpretation of your results?

Reject the null hypothesis

Assume that you have conducted a t test with matched samples. Your test is based upon the before and after scores of 15 research participants, and you have selected the .05 level of significance. You have calculated your test statistic; it is equal to 2.216. Using Appendix B to find the appropriate critical value, which of the following would be the proper interpretation of your results?

Reject the null hypothesis, with the knowledge that there is a 5% probability of having made a Type I error

Assume two matched samples, each involving 14 subjects (n = 14) and the following information: Mean of the differences (D̅) = 3.42 Standard deviation of the differences (sd) = 3.46 Recall the formula for determining the estimated standard error of the mean using n and sd. Calculate t. Assuming a .05 level of significance (α = .05), do you reject or fail to reject the null hypothesis?

SD = 3.46 / sq rt of 14 = .93 Calculated test statistic: t = 3.42 / .93 = 3.68 Critical value: t = 2.160 Reject the null hypothesis.

How do you calculate the number of degrees of freedom for the hypothesis test involving independent samples (Sample A and Sample B)?

The degrees of freedom would be equal to the number of cases in Sample A, minus 1, plus number of cases in Sample B, minus 1. .

How do you calculate the number of degrees of freedom for the hypothesis test involving two matched or related samples?

The degrees of freedom would be equal to the number of differences (i.e., the string of d values) that you calculated, minus 1.

A researcher conducts a t test for related samples and calculates a value of t = 3.24. For the researcher conducting the research, the value of t = 3.24 is a statement of:

the calculated test statistic

SD =Sd/square root of n is the formula that represents:

the estimate of the standard error of the mean difference

SX1 - X2 is the symbol that represents:

the estimate of the standard error the difference between means

A hypothesis test is used to determine if there is a difference between scores made on a reading comprehension test before and after the students hear a series of lectures in a Reading to Retain program. The hypothesis test in a situation like that would involve:

the notion of a sampling distribution of mean differences

You want to determine if there is a change in perception of voters following exposure to a commercial about Candidate X. Accordingly, you select a sample of 20 registered voters, and you measure the attitude of each voter before and after exposure to the film by asking each voter to assign the candidate an approval score from 0 to 100. Your test is actually based on:

the notion of a sampling distribution of mean differences

A test to determine if there is a difference between liberal arts and business majors in terms of their scores on a current events test is conducted using a sample of 40 liberal arts majors and a sample of 25 business majors. The test is actually based on:

the notion of a sampling distribution of the difference between means