Solutions Statistics

A survey asked 2000 people whether or not they frequently exceed the speed limit. The collected data

Question: A survey asked 2000 people whether or not they frequently exceed the speed limit. The collected data is summarized in the following contingency table. The goal is to determine if there is a difference in the population proportion that say “yes” when comparing those who are under 40 years in age to those who are at least 40 years in age.

Table A.1. Data Summary

	Frequently Exceed the Speed Limit?
Age	Yes	No	Total
Age under 40	600 (60%)	400	1000
Age 40 and above	450 (45%)	550	1000
Total	1050	950	2000

a. What is the response variable in this problem?

b. What is the explanatory variable in this problem?

c. What type of variable is the response variable? categorical or measurement

d. What is the appropriate population value for this problem? population mean or population proportion

e. Write out the null and alternative hypotheses in terms of the appropriate population value.

f. On the output found in Figure A.2 the test statistic is 6.72. Use this test statistic to write out a one-sentence interpretation of the p-value.

g. What conclusion can be made in terms of this problem? Why?

h. Compare the sample percent (proportion) that said yes for the two age groups that are found in Table A.1. Do you believe the results are practically significant? Include reasoning.

i. Could a Chi-square Test also be used to analyze this data? (Hint: Refer back to lesson assignments in Lesson 7.)

Test and CI for Two Proportions

Sample X N Sample p

< 40 yrs 600 1000 0.60

≥ 40 yrs 450 1000 0.45

Estimate for p(1) - p(2): 0.15

95% CI for p(1) - p(2): (0.107, 0.193)

Test for p(1) - p(2) = 0 (vs not = 0): Z = 6.72 P-Value = 0.000

Figure A.2.

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