Social
Studies 201
Winter, 2001
Final Examination
2 – 5 p.m. – Wednesday, April 18, 2001, CL420.
Answer any three (3) questions. Each question has equal value.
1. Hours at Jobs for Students. The data in Table 1 come from the Survey of Student Attitudes and Experiences, Fall 1998. Assume that these data represent a random sample of University of Regina undergraduates with jobs.
a. Test whether the mean weekly hours worked for all University of Regina undergraduate males with jobs exceeds 20 hours per week. Test whether the mean weekly hours for females differs from 20 hours per week.
b. Obtain 92% confidence interval estimates for the true mean weekly hours of work at jobs for each of male and female undergraduates with jobs.
c. Briefly explain the meaning of the results in a. and b. In particular, comment on whether the results from the interval estimates are consistent with the results from the hypothesis tests and whether male and female hours at work differ. Also indicate any possible errors in the results.
Table 1.
Weekly Hours at Jobs for University of Regina Undergraduates with Jobs,
Fall, 1998
Sex 
Mean Weekly Hours 
Standard Deviation of Weekly Hours 
Sample Size 
Male 
22.1 
12.8 
143 
Female 
18.9 
11.1 
245 
Total 
20.1 
11.8 
388 
2. Stress Levels. In the Survey of Student Attitudes and Experiences, Fall 1998, students were asked to state how much stress they experienced related to academic performance and to relationships with parents. Responses were coded on a 3point scale with 1 as minimal stress, 2 as medium stress and 3 as high stress. Results for two samples of undergraduates are shown in Table 2.
Table 2. Statistics on Stress Levels of Undergraduates for Reasons Related to Academic Performance and Relations with Parents
Sample 
Statistic 
Academic Performance 
Relations with Parents 
Sample 1 
Mean 
2.24 
1.45 
Standard Deviation 
0.77 
0.76 

Sample Size 
21 
20 

Sample 2 
Mean 
2.36 
1.35 
Standard Deviation 
0.66 
0.61 

Sample Size 
697 
694 
a. On the academic performance issue, for each of the two samples test whether the mean stress level for all students exceeds 2 (medium stress). Use the 0.05 level of significance. Explain why the result differs for the two samples.
b. On the relations with parents issue, for each of the two samples, obtain 95% interval estimates for the true mean stress level. Explain why the intervals differ in interval width.
c. For any such issue, how large a sample size would be required to obtain the true mean level of stress for all undergraduates, correct to within 0.1 points on the 3point scale, with 99% confidence?
3.
Feelings About Finances – Large Sample Size. In the General
Social Survey 1998, Cycle 12, conducted by Statistics Canada, respondents
were asked to rate their feeling concerning how satisfied they were with their
finances. The responses of the
Saskatchewan respondents to this question are given in Table 3. The means and standard deviations are also
given, using the 14 scale identified in the left column of the table.
Table 3. Responses
of Saskatchewan Males and Females to Question Concerning Feeling About their
Finances
Response 
Male 
Female 
Total 
Very Satisfied (1) 
63 
67 
130 
Somewhat Satisfied (2) 
139 
170 
309 
Somewhat Dissatisfied (3) 
66 
89 
155 
Very Dissatisfied (4) 
26 
41 
67 
Total 
294 
367 
661 
Mean 
2.19 
2.28 
2.24 
Standard Deviation 
0.87 
0.89 
0.88 
a. Test whether the mean response for all Saskatchewan males differs from 2.5. Conduct the same test for females.
b. For each of male and females in the province, test whether the proportion who are satisfied with their finances exceeds onehalf.
c. From a. and b., comment on whether respondents appear to be generally satisfied with their finances.
4. Feelings About Finances – Small Sample Size. From the same survey as in question 3, a sample of 8 respondents from Saskatchewan shows that 1 respondent is very satisfied, 4 are somewhat satisfied, and 3 are somewhat dissatisfied with their finances.
a. Using the same coding as in Table 3, obtain the mean and standard deviation of responses for this sample of size 8.
b. Using this sample of size 8, test whether the mean response of Saskatchewan respondents differs from 2.5.
c. How large a sample size would be required to obtain the true mean response for any group correct to within 0.25 points on the 14 scale, with probability 0.95?
5. Importance of Issues. In Unknown Gods: the Ongoing Story of Religion in Canada, (pp. 139 and 143), Reginald W. Bibby of Lethbridge University provides the data in Table 4. Bibby obtained these results from surveys of adults across Canada. Of these data, Bibby notes that physical issues become less important with age, “intellectual growth also ceases to know the importance it did earlier in life” and “the one area in where there is a shift in the direction of increases in importance with the passage of time? God.”
Table 4. Importance of Various Issues to Canadians
Aged 1824 and 3544
Issue Identified as More Important 
Per Cent of each Age Stating Increased Importance 

Ages 1824 
Ages 3544 

Sex 
61% 
25% 
Intellectual Growth 
71% 
45% 
Spiritual Issues 
23% 
31% 
Sample Size 
107 
249 
Use the data in Table 4 to answer the following:
a. Obtain interval estimates for the proportion of respondents of each of the two age groups who identify spiritual issues as of increased importance.
b. Test whether the proportion of those of age 1824 who identify sex as of increased importance exceeds onehalf.
c. How large a sample size would be required to obtain the proportion of respondents who identify any issue as of increased importance, correct to within 5 percentage points, 18 times in 20.
d. Briefly comment on Bibby’s statement using the data in Table 4 and the results from a. and b.
6. Economic Situation over the Next Year. The data in Tables 5 and 6 come from an IpsosReid poll released on March 30, 2001. The question was “What about you and your family? Do you feel that your own economic situation will improve, stay the same, or get worse over the next year?” Table 5 shows the number of respondents for each age group and Table 6 gives the data for the chisquare analysis of the data in Table 5.
a. Obtain 95% interval estimates for the proportion of respondents of each age group who think that the situation will get worse.
b. Use the data in Table 6 to test whether response to this question and age of respondent are dependent on each other. (0.001 level of significance).
c. Write a short note comparing the results in a. and b. and the pattern of response by age.
Table
5. Evaluation of economic situation over next year, by age, Canada
Response 
Age of Respondent 
Total 

1834 
3554 
55 plus 

Improve 
142 
104 
35 
281 
Stay the same 
146 
241 
155 
542 
Get worse 
43 
69 
46 
158 
Total 
331 
414 
236 
981 
Source: IpsosReid Poll of March 30, 2001
Table 6. ChiSquared
Results for Data in Table 5
Expected counts are printed below observed counts
1834
3554 55 plus
C1 C2 C3 Total
Improve 1 142 104 35 281
94.81 118.59 67.60
Stay Same 2
146 241 155
542
182.88
228.73 130.39
Get Worse 3
43 69 46
158
53.31
66.68 38.01
Total 331 414
236 981
ChiSq = 23.485 +
1.794 + 15.722 +
7.436 +
0.658 + 4.645 +
1.994 +
0.081 + 1.679 = 57.494
df = 4