Questions

1. A statistics tutor wants to assess whether her remedial tutoring has been effective for her five students. She decides to conduct a related samples t-test and records the following grades for students prior to and after receiving her tutoring.

Tutoring
Before	After
2.6	3.3
2.7	3.0
3.2	3.8
3.1	3.3
2.9	3.8

(a) Test whether or not her tutoring is effective at a 0.05 level of significance. State the value of the test statistic. (Round your answer to three decimal places.) t = State the decision to retain or reject the null hypothesis.

Retain the null hypothesis. Reject the null hypothesis.    

(b) Compute effect size using estimated Cohen's d. (Round your answer to two decimal places.) d =

2. A psychologist wants to know whether wives and husbands who both serve in a foreign war have similar levels of satisfaction in their marriage. To test this, six married couples currently serving in a foreign war were asked how satisfied they are with their spouse on a 7-point scale ranging from 1 (not satisfied at all) to 7 (very satisfied). The following are the responses from husband and wife pairs.

Married Couples
Wife	Husband
7	5
3	6
7	5
7	6
7	5
6	5

(a) Test whether or not mean ratings differ at a 0.05 level of significance. State the value of the test statistic. (Round your answer to three decimal places.) State the decision to retain or reject the null hypothesis.

Retain the null hypothesis. Reject the null hypothesis.    

(b) Compute effect size using eta-squared. (Round your answer to two decimal places.)

3. Listening to music has long been thought to enhance intelligence, especially during infancy and childhood. To test whether this is true, a researcher records the number of hours that eight high-performing students listened to music per day for 1 week. The data are listed in the table.

Music Listening Per Day (in hours)
4.1
4.8
5.1
3.7
4.2
5.4
4.0
4.4

(a) Find the confidence limits at a 95% CI for this one-independent sample. (Round your answers to two decimal places.) to hours per day (b) Suppose the null hypothesis states that students listen to 3.5 hours of music per day. What would the decision be for a two-tailed hypothesis test at a 0.05 level of significance?

Retain the null hypothesis because the value stated in the null hypothesis is within the limits for the 95% CI.

Reject the null hypothesis because the value stated in the null hypothesis is outside the limits for the 95% CI.    

Reject the null hypothesis because the value stated in the null hypothesis is within the limits for the 95% CI.

Retain the null hypothesis because the value stated in the null hypothesis is outside the limits for the 95% CI.

4. To save money, a local charity organization wants to target its mailing requests for donations to individuals who are most supportive of its cause. They ask a sample of 5 men and 5 women to rate the importance of their cause on a scale from 1 (not important at all) to 7 (very important). The ratings for men were

M1 = 6.4.

The ratings for women were

M2 = 5.2.

If the estimated standard error for the difference

(sM1 − M2)

is equal to 0.25, then consider the following.

(a) Find the confidence limits at an 80% CI for these two-independent samples. (Round your answers to two decimal places.) to (b) Can we conclude that men or women are more supportive to their cause? Explain.

Yes, the lower and upper limits of the confidence interval are positive, indicating that mean ratings of importance are higher for the population of men compared to women.

Yes, the lower and upper limits of the confidence interval are negative, indicating that mean ratings of importance are higher for the population of women compared to men.  

   No, the lower and upper limits of the confidence interval contain zero, indicating that mean ratings of importance may not be higher for the population of men or women.

No, the lower and upper limits of the confidence interval are negative, indicating that mean ratings of importance may not be higher for the population of men or women.

5. An instructor believes that students do not retain as much information from a lecture on a Friday compared to a Monday. To test this belief, the instructor teaches a small sample of college students some preselected material from a single topic on statistics on a Friday and on a Monday. All students received a test on the material. The differences in exam scores for material taught on Friday minus Monday are listed in the following table.

Difference Scores (Friday − Monday)

−1.5

+6.3

+3.3

+0.9

+4.4

(a) Find the confidence limits at a 95% CI for these related samples. (Round your answers to two decimal places.) to (b) Can we conclude that students retained more of the material taught in the Friday class?

Yes, because 0 lies outside of the 95% CI. No, because 0 is contained within the 95% CI.   

 

6. Jamieson and Romer (2008) evaluated children's beliefs concerning life expectancy in a diverse sample of American children. In their study, they reported at a 95% CI that "approximately 1 out of every 15-youth interviewed (6.7% [5.9%, 7.5%]) responded that they agreed they would not live much past the age of 30."†

(a) What is the point estimate and interval estimate for these data?

point estimate		%
interval estimate		% to %

(b) If these researchers computed an 80% CI, how would this change the precision and certainty of their estimate?

The estimate would be more precise but less certain. The estimate would be less precise but more certain.     The estimate's precision and certainty would not change. The estimate would be more precise and more certain. The estimate would be less precise and less certain.

6.