Social Studies 201

Fall 2003

Problem Set No. 5

# Due:  December 1, 2003

1. Use of media – Table 1.

a.       Obtain 96% interval estimates for the true mean minutes of media use daily by all Saskatchewan respondents (i) aged 15-24 and (ii) aged 55-64.  From these, does it seem likely that 55-64 year olds use the media more than do 15-24 year olds?

1. Using the data in the last row of Table 1, obtain a 99% interval estimate for the true mean media use daily for all Saskatchewan adults.  Explain why the width of this interval differs from the width of the intervals in a.

Table 1.   Sample sizes, means, and standard deviations of minutes spent daily using media by Saskatchewan respondents of various ages

 Age Sample Size Mean Minutes Daily Standard Deviation of Minutes Daily 15-24 80 168 128 25-34 113 154 123 35-44 115 180 137 45-54 84 179 133 55-64 88 202 160 65-74 81 280 183 75-84 51 336 195 85+ 19 334 239 Total 631 207 162

Source: Statistics Canada, General Social Survey, Cycle 12: Time Use, 1998

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.

1. For sample 1, obtain a 98% interval estimate for the true mean stress level, for all undergraduates, on the relations with parents issue.
2. 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.
3. 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?

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

3. 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 3.  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.”   Use the data in Table 3 to answer the following:

1. Obtain interval estimates for the proportion of adults 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.

1. 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.
2. Briefly comment on Bibby’s statement using the data in Table 3 and the results from a. and b.

## Table 3. 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 Ages 18-24 Ages 35-44 Sex 61% 25% Intellectual Growth 71% 45% Spiritual Issues 23% 31% Sample Size 107 249

4. Computer problems to be handed out on Monday, November 17.