Social Studies 201

Social Studies 201 – Winter, 2001

Problem Set 5

Due Monday, April 9, 2001

1. Views on Multiculturalism. Two attitude questions on multiculturalism from a sample of University of Regina undergraduates in the Survey of Student Attitudes and Experiences, Fall 1998 gave the results in Table 1.

Table 1. Responses to Questions on Multiculturalism

Response	Number of Respondents
Response	Diversity Fundamental	Fund Festivals
Strongly disagree – 1	1	2
Disagree – 2	1	5
Neutral – 3	3	2
Agree – 4	2	5
Strongly agree – 5	11	4
Total	18	18
Mean	4.17	3.22
sd	1.25	1.40

a. What are the 90% and 98% interval estimates for the true mean responses to each of these questions for all University of Regina undergraduates?

b. How large a sample size would be required to estimate the true mean response to one of these attitude questions correct to within 0.1 points, at 90% confidence level.

c. An average response of 3 (middle of the 1 to 5 scale) could be considered a neutral response. At the 0.05 level of statistical significance, test whether the mean response on the funding festivals question differs from 3. Also test whether the mean response on the diversity fundamental question exceeds 3 at the 0.01 level of significance.

2. Student Debt Load. The data in Table 2 come from the Survey of Student Attitudes and Experiences, Fall 1998. Use these data to test and comment on the following assertions.

a. A student advocate claims that university funding has been cut so that that the mean university student debt load increased by over $5,000 in one year. Use the summary data in the right column to test this contention (0.10 level of significance).

b. A politician from the North West Party claims that there was not a crisis in university funding since over two-thirds of students had no increase in debt load in 1998-1999. Test whether the proportion of students with no increase in debt load exceeded two-thirds (0.05 level of significance).

c. What might you conclude about student debt loads from the above tests and the data in Table 2?

Table 2. Change in Debt of University of Regina Undergraduates, 1998-1999

Change in Debt During 1998-1999 (in dollars)	Number of Students
Less than 0	10
0	397
0-2,499	38	For those whose debt increased, the mean increase was $5,275 with a standard deviation of $3,689 .
2,500-4,999	39
5,000-9,999	68
10,000 plus	22
Total	574
Mean	1,511
Standard Deviation	3,132

3. Government Budget Priorities. The data in Table 3 represent the responses to the question “Should the first priority of government be to use the surplus to cut income taxes, increase spending on programs like health care and education, or reduce the government debt?” The data were produced from an October, 2000 poll by Decima Research Inc., conducted for the Canadian Association of University Teachers.

Table 3. Responses to Question on Use of Surplus. Manitoba, Saskatchewan, Alberta, and Canada

Response	Manitoba/Saskatchewan	Alberta	Canada
Cut income taxes	28	40	428
Increase spending on programs such as health care and education	72	75	1,058
Reduce government debt	38	66	496
Total	138	181	1,982

a. Table 4, Decima Express Methodology comes from the same survey as that noted in Table 3. Using the formulae for interval estimates for proportions, obtain what Decima calls the “error intervals” for Manitoba/Saskatchewan, Alberta, and Canada. What is missing from Decima’s description of the error intervals?

b. What would be the sample size required in Saskatchewan in order to achieve an interval no more than 2 percentage points wide, with 90% confidence?

c. From Table 3, obtain the 99% interval estimates for the proportion of Manitoba/Saskatchewan residents who support reducing the government debt? Why is this interval wider than Decima’s “error interval” for Manitoba/Saskatchewan?

Table 4. Decima Express Methodology

4. Computer Problems on Hypothesis Tests

This problem set asks you to obtain some interval estimates and test some hypotheses using the 372.mtw file. Once in MINITAB, use File – Open Worksheet – Select File and then find your way to t:\students\public\201 and obtain the 372.mtw file. After doing this, type info and press the Enter key to see that you have in fact obtained the correct file.

a. Tests of Hypothesis.

Use Stat – Basic Statistics – 1 Sample t to conduct the following hypothesis tests.

i. Test whether the mean of V4 equals 3, the midpoint of the attitude scale that runs from 1 to 5.

ii. Test whether the mean of V4 equals 3.1.

iii. Test whether the mean of V4 equals 3.2.

iv. Test whether the mean of V4 equal 3.5.

v. Test whether the mean GPA equals 75 and then test whether the mean GPA equals 74.

b. From the MINITAB output, answer the following:

In words, describe the results of the tests in (a) (i)-(iv). From these tests and the interval estimates for V4 in question 1, what might you conclude concerning the true value of the mean opinion on V4 for all University of Regina undergraduates?

What do you conclude concerning the mean GPA for all University of Regina undergraduates?

c. Cross-Classifications.

Use Stat-Tables-Cross Tabulation to obtain the following cross-classification tables and the associated chisquare analysis for each of the two tables.

i. Cross-classification of provote by future.

ii. Cross-classification of sex by future.

d. Comment.

Using the tables in c. and the chi-square statistic on the MINITAB printout, explain whether (i) future is independent of provote, and (ii) sex is independent of (ii) future. Also calculate the chi-square value by hand for table c. ii. and check to see that your chi-square value matches the value from the printout.