Social Studies 201

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 3-point 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 3-point 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 1-4 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 one-half.

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 1-4 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 18-24 and 35-44

Issue Identified as More Important	Per Cent of each Age Stating Increased Importance
Issue Identified as More Important	Ages 18-24	Ages 35-44
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 18-24 who identify sex as of increased importance exceeds one-half.

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 Ipsos-Reid 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 chi-square 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
Response	18-34	35-54	55 plus	Total
Improve	142	104	35	281
Stay the same	146	241	155	542
Get worse	43	69	46	158
Total	331	414	236	981

Source: Ipsos-Reid Poll of March 30, 2001

Table 6. Chi-Squared Results for Data in Table 5

Expected counts are printed below observed counts

18-34 35-54 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