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
onequarter 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 2024 with one or more children in the household, or (ii)
Saskatchewan females aged 2024 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 AnalyzeDescriptive StatisticsExplore 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 AnalyzeCompare MeansOneSample Ttest.
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 AnalyzeCompare MeansOneSample Ttest 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.
Characteristics
of members of the group 
Statistics of daily hours of sleep 
Sample size 

Mean 
Standard deviation 

Males,
2024, 1+ child 
6.25 
1.14 
12 
Females.
2024, 1+ child 
6.84 
1.34 
25 
Source: Statistics Canada. Canadian Community Health
Survey, Cycle 1.1 (20002001) [machine readable data file]. Release 2 Edition.
Ottawa, ON: Statistics Canada. July 23, 2003.
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.”