Question

PLEASE ANSWER ALL BEFORE SUBMITTING. THANK YOU. "___" = answers needed.

4. What are the difference scores for the following list of scores for participants observed at two times?

Time 1	Time 2	Time 1 − Time 2
10	8	____
3	2	____
6	7	____
5	6	____
7	3	____

6. A statistics individual wants to assess whether her remedial job 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 job.

Tutoring
Before	After
2.6	3.2
2.7	3.1
3.2	3.7
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 = ___
(B) Compute effect size using estimated Cohen's d. (Round your answer to two decimal places.)
d = ___

7. 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
6	5
4	6
7	5
6	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.) ___
(B) Compute effect size using eta-squared. (Round your answer to two decimal places.) ___

9. A researcher records the amount of time (in minutes) that parent-child pairs spent on social networking sites to test whether they show any generational differences. From the following findings reported in APA format, interpret these results. Parents spent significantly less time on social networking sites compared to their children (M_D = 42 minutes), t(19) = 3.476, p < 0.05, d = 0.59.

State the sample size.
___ participants

16. 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)
4.3
4.9
4.9
3.8
4.2
5.4
4.2
4.5

(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

17. 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 = 6.3. The ratings for women were M₂ = 5.4. If the estimated standard error for the difference (s_{M1 − 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 ___

18. 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 scores for material taught on Friday minus Monday are listed in the following table.

Difference Scores (Friday − Monday)
−1.7
+1.0
+6.4
+3.5
+4.5

(A) Find the confidence limits at a 95% CI for these related samples. (Round your answers to two decimal places.)
___ to ___

Answer 1

4) The difference of scores of the participants for the two time points is displayed in the table as follows-

Score at Time 1 (X)	Score at Time 2 (Y)	Difference of scores at Time 1 and Time 2 X-Y
10 3 6 5 7	8 2 7 6 3	2 1 -1 -1 4

6)

Grade after tutoring Xi	Grade before tutoring Yi	Difference in the Grades of after and before di = Xi - Yi
3.2 3.1 3.7 3.3 3.8	2.6 2.7 3.2 3.1 2.9	0.6 0.4 0.5 0.2 0.9	0.0064 0.0144 0.0004 0.1024 0.1444
		= 2.6	=0.268

Sample Mean difference,  

Sample standard deviation of the difference,

a) Hypotheses can be framed as -

Null hypothesis : Tutoring of the statistical individual has no effect in improving the grades of the students.

i.e the mean difference between the grades of students after and before her tutoring  is zero.

Alternative hypothesis : Tutoring of the statisrstat individual has improved the grades of students.

i.e the mean difference between the grades of students after and before her tutoring is greater than zero.

Test statistic is given by -

where, is the sample mean difference in the grades after and before her tutoring = 0.52

is the hypothesed value of the population mean difference in the grades after and before her tutoring under the null hypothesis = 0

is the sample standard deviation of the mean difference = 0.067

n is the sample size = 5

Putting all these values in the formula of test statistic, we get,

= 17.354

Critical value of t with 4 degrees of freedom and 0.05 level of significance is 2.132 (as obtained from the t table corresponding to the 0.05 probability and 4 degrees of freedom)

Since value of the test statistic > critical value of t, we may Reject the null hypothesis, hence, the tutoring of the statistical individual improved the grades of students.

b) Cohen's d effect size is given by,

= 7.76

Since, effect size d > 0.8, hence, effect size is large.