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.
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.
3. Opinions about selling Petro-Canada. On March 30 and April 1, 2004, the Ipsos-Reid market research and public opinion polling firm telephoned a randomly selected sample of 1,057 adult Canadians. Respondents were asked whether they agreed or disagreed with the statement, “The Canadian federal government should not sell all its shares in PetroCanada as recently announced, but rather it should continue to have part ownership of PetroCanada because it is important to maintain Canadian ownership and influence to ensure Canada’s energy security in the future.” Ipsos-Reid reported “Canadians want continued government ownership of PetroCanada. Some of the results of the poll are presented in Table 2.
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.