# Due April 8, 2005

1.  Interval estimates

a.       From Table 1, obtain a 85% interval estimate for the mean age at first marriage (i) for all Saskatchewan males in 2001; and (ii) for all Saskatchewan females in 2001.  In 1976 the mean age at marriage for Canadian males was 27.9 years and for Canadian females was 25.3 years.  From the interval estimates, explain whether age at marriage appears to have changed since 1976.

b.       From the data in Table 2, obtain 90% interval estimates of mean hours of sleep daily for (i) males and (ii) females.  From the data in Table 2 and the interval estimates, what can you conclude about the mean hours males and females sleep each day?

c.       Using the survey results in Table 3, obtain a 94% interval estimate for the proportion of Quebec residents who are satisfied (very or somewhat) with the agreement.  Obtain the corresponding interval estimate for the rest of Canada.  From these interval estimates, what can you conclude about differences of opinion between Quebec and the rest of Canada on this  issue.

2.  Sample sizes

a.       Using the information from Table 2, how large a sample size would be required to determine the mean number of hours a group sleeps, correct to within one-quarter hour, eighteen times in twenty?  Within five minutes, eighteen times in twenty?

b.       Referrring to the survey data in Table 3, Environics reports that the “survey was conducted by telephone among a representative sample of 2,027 adult Canadians … A sample of this size has a margin of error of plus or minus 2.2 percentage points, 19 in 20 times.”  Using a formula from the class, verify this statement.   Obtain the comparable margin of error for (i) Quebec and (ii) rest of Canada.

3.  Hypothesis tests

a.       In 1976 the mean age at marriage for Canadian males was 27.9 years and for Canadian females was 25.3 years.  Using the data in Table 1, test whether the mean age at first marriage for Saskatchewan males in 2001 differed from the mean age reported for Canadian males in 1976.  For Saskatchewan females, test whether the mean age at first marriage in 2001 was lower than the Canadian mean for females in 1976.  Clearly state your hypotheses and conclusions.  (0.10 significance in each case).

b.       Test whether there is sufficient evidence to conclude that either (i) Saskatchewan males aged 20-24 with one or more children in the household, or (ii) Saskatchewan females aged 20-24 with one or more children in the household, sleep less than seven hours per day, on average.  Test each hypothesis at the 0.05 level of significance, using the statistics in Table 2.

c.       It appears that approximately eighty per cent of Canadians are satisfied (very or somewhat) with the health agreement.  Using the survey results in Table 3, test whether (i) the proportion of Quebec residents who are satisfied (very or somewhat) differs from 0.8 or 80%; (ii) the proportion of residents in the rest of Canada who are satisfied (very or somewhat) exceeds 0.8.  (0.10 significance in each case).

4.  Computer problem on interval estimates and hypothesis tests.  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 UED4, responses to the statement “University education should be made more accessible by lowering tuition.”  (question 50 of the SSAE98 questionnaire).

i.  Obtain the 95% interval estimate for UED4.

ii.  Obtain the 97% interval estimates for UED4, classified by sex of respondent (in factor list).

iii.  Obtain the 90% interval estimates for UED4, classified by FV, federal political party preference.

b. Describe the results, commenting on what you can conclude about differences in opinion about reducing tuition among the different groups.

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

i.  Test whether the mean hourly pay for University of Regina undergraduates with jobs differs from \$10.00 per hour.

ii.  Test whether the mean debt for University of Regina undergraduates at the start of the Fall 1998 semester (DEBT1) is less than \$4,000.   Then test whether the mean debt is expected to exceed \$4,000 by the end of the Winter, 1999 semester (DEBT2).

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 of weekly hours University of Regina students spent studying (i) exceeds 15 hours, (ii) differs from 16 hours, (iii) differs from 17 hours, and (iv) is less than 18 hours.

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

Table 1.  Statistics of age at first marriage, Saskatchewan, 2001

 Characteristic Sex of respondent Male Female Mean age 27.52 24.67 Standard deviation of age 8.07 7.68 Sample size 321 352

Source:  2001 data from Statistics Canada. General Social Survey of Canada, 2001. Cycle 15: Family History (Union file) [machine readable data file]. Ottawa, ON: Statistics Canada. 4/23/2003.  1976 data from Roderic Beaujot and Kevin McQuillan, Growth and Dualism, Gage Publishing Limited, Toronto, 1982, p. 132.

## Table 2.  Hours of sleep daily reported by respondents with different characteristics, Saskatchewan, 2001

 Characteristics of members of the group Statistics of daily hours of sleep Sample size Mean Standard deviation Males, 20-24, 1+ child 6.25 1.14 12 Females. 20-24, 1+ child 6.84 1.34 25

Source:  Statistics Canada. Canadian Community Health Survey, Cycle 1.1 (2000-2001) [machine readable data file]. Release 2 Edition. Ottawa, ON: Statistics Canada. July 23, 2003.

## Table 3.  Percentage distributions of views about the September 2004 health agreement.  Canada, Quebec, and rest of Canada

 View or opinion concerning health agreement Percentage of respondents with each view in: Canada Quebec Rest of Canada Very satisfied 18 22 16 Somewhat satisfied 62 54 65 Neutral 2 5 1 Somewhat dissatisfied 14 14 14 Very dissatisfied 4 5 4 Total 100 100 100 Sample size 2,027 498 1,529

Source:  Environics Research Group, “Majority Satisfied with Health Agreement,” 10/19/2004, http://erg.environics.net/news/default.asp?aID=568.

Note:  These are results from an Environics Research Group survey, conducted in late September and early October 2004, that reported “Majority Satisfied with Health Agreement.”