# Social Studies 201

Fall 2004

Problem Set 5

Due December 1, 2004

1.  Hours worked for Saskatchewan and Canadian adults.  The data in Table 1 come from a sample of Saskatchewan adults who had full-time and full-year jobs.  The data refer to annual hours worked at these jobs in 1999.

1. Construct a 92% interval estimates for mean annual hours worked at jobs for (i) all Saskatchewan male workers and (ii) all Saskatchewan female workers.
2. How large a sample size would be required to estimate the true mean hours worked for any group of full-time, full-year workers correct to within plus or minus (i) 50 hours and (ii) 25 hours, with 95 per cent confidence?
3. In 1999, mean hours worked at jobs for Canadian, full-time, full-year male workers was 2,169 hours and for female workers was 1,917 hours.  Using data from Table 1, test whether Saskatchewan (i) male workers and (ii) female workers work more hours at jobs than do Canadian workers.  Use 0.01 significance.

Table 1.  Means, standard deviations, and sample sizes of annual hours worked at jobs, sample of Saskatchewan adults with full-time, full-year jobs, 1999

 Sex of adult Annual hours worked at jobs Sample size Mean Standard deviation Male 2234 683 1002 Female 1975 458 738 Total 2124 611 1,740

Source:  Statistics Canada. Survey of Labour and Income Dynamics (SLID), 2000: Person file [machine readable data file]. Ottawa, ON: Statistics Canada. 7/16/2003.

2.  Annual wages and salaries.  From the same survey as used in question 1, the mean annual wages and salaries of full-time, full-year Canadian workers was \$35,024 in 1999.

A small random sample of eight Saskatchewan adults who worked full-time, full-year in 1999 gave the following annual wages and salaries (in thousands of dollars):  55, 39, 5, 16, 12, 22, 58, and 49.  Calculate the mean and standard deviation for this sample and use these statistics for the following.

1. Obtain the 90% and 99% interval estimates for the mean annual wages and salaries for all Saskatchewan workers who worked full time, full-year in 1999.
2. Test whether these data provide sufficient evidence to conclude that Saskatchewan workers have lower wages and salaries than their Canadian counterparts.  (0.05 level of significance).
3. Compare the results of a. and b., commenting on any possible errors in your conclusions.

Table 2.  Percentages and sample sizes for Canadian and Saskatchewan/Manitoba respondents expressing each view concerning not selling PetroCanada

 View on not selling PetroCanada Per cent of respondents with each view Canada Saskatchewan/Manitoba Strongly agree 48% 36% Somewhat agree 27% 36% Somewhat disagree 11% 16% Strongly disagree 14% 12% Total 100% 100% Sample size 1,057 100

Source:  http://www.ipsos-na.com/news/pressrelease.cfm?id=2122, obtained April 18, 2004.

a.       Using the data in Table 2, obtain 97% interval estimates for the true proportion of all (i) Canadian adults and (ii) Saskatchewan/Manitoba adults who agree (strongly or somewhat) that PetroCanada should not be sold.

b.      Ipsos-Reid reports “Three-quarters of Canadians do not think that the federal government should sell all of its PetroCanada shares.”  Using the poll results from Saskatchewan/Manitoba, test where adults in Saskatchewan and Manitoba are less in agreement with not selling PetroCanada than their counterparts across Canada as a whole.  (0.10 significance).

c.       From a. and b., and Table 2, comment on any differences between the results for Saskatchewan/Manitoba and Canada.

d.      Ipsos-Reid states “With a sample of this size, the results are considered accurate to within ± 3.1 percentage points, 19 times out of 20, of what they would have been had the entire adult Canadian population been polled. The margin of error will be larger within regions and for other sub-groupings of the survey population.”  Verify the plus or minus 3.1 percentage points.  Show your work.  What is the comparable margin for Saskatchewa/Manitoba?

4.  Computer problem.  Use the SSAE98 data set (in folder t:\students\public\201) to obtain the following.  Print out the results for the a. parts of each question and write the answers to the b. parts on the printout.  Alternatively, use Copy objects to move the tables into a Word for Windows file, write the answers to the b. parts there, and then hand in.

1.  a.  Use Analyze-Descriptive Statistics-Explore with Statistics selected and Plots deselected to obtain the following interval estimates for V4, responses to the statement “Tax laws and job benefits should recognize gay and lesbian couples as married.”  (question 15).

i.  Obtain the 95% interval estimate for V4.

ii.  Obtain the 98% interval estimates for V4, classified by sex of respondent (in factor list).

iii.  Obtain the 90% interval estimates for V4, classified by PV, provincial political party preference (2nd last variable on variable list).

b. Describe the results, commenting on what you can conclude about differences in opinion about treating gay and lesbian couples as married.

2.  a.  Obtain the following using Analyze-Compare Means-One-Sample T-test.

i.  The mean weekly hours Canadian post-secondary students with jobs report spending at their jobs is 17.2 hours. (See Sandra Franke, “Studying and working: The busy lives of students with paid employment,” Canadian Social Trends, Spring 2003, pp. 22-25).   Test whether University of Regina students spend a different amount of time at paid jobs than do their counterparts across the country.

ii.  From the Statistics Canada survey, General Social Survey of Canada 1998 – Cycle 12, the mean household income for all Saskatchewan residents was \$55,100, and for all Ontario residents was \$62,000.  Test whether the mean income for the households or families of students (income in thousands of dollars – INC) exceeds mean income for each of the two provinces.

b.  Explain the findings from part a.  In doing this, make sure you mention the null and research hypotheses, the significance level, and your conclusions.

3.  a.  Use Analyze-Compare Means-One-Sample T-test to test whether the mean student debt after winter 1999 (i) exceeds \$4000, (ii) differs from \$4,500, (iii) differs from \$5000, and (iv) is less than \$5,500.

b.  Write a short description of what you conclude from a.