Quiz: Test for Comparing Two Proportions

1. One method for estimating the standard error of the sampling distribution for the difference of two proportions uses a pooled, or combined, proportion. Which statement best describes the use of the pooled proportion?
a. the pooled proportion is used for a hypothesis test because the null hypothesis states that the two population proportions are equal
b. the pooled proportion is used for a confidence interval because it is an estimate of the difference of the proportions
c. the pooled proportion is a superior estimate for both hypothesis tests and confidence intervals
2. Which is the best estimate of the standard deviation of the sampling distribution for the difference in population proportions for a confidence interval?
a. equation
b. equation
c. equation
3. Which is the best estimate of the standard deviation of the sampling distribution for the difference in population proportions for a hypothesis test?
a. equation
b. equation
c. equation
4. Two random samples are selected to test if there is a difference in two population proportions. Which is not a correct null hypothesis?
a. H0: π1 = π2
b. H0: π1 – π2 = 0
c. H0: π1 ≠ π2
5. Two random samples are selected to test if there is a difference in two population proportions. Which is the best alternate hypothesis?
a. Ha: π1 > π2
b. Ha: π1 < π2
c. Ha: π1 ≠ π2

Two random samples are selected to test if there is a difference in two population proportions with a = 0.05 level. The results are, equation, n1 =50, equation, and n2 = 40. Use this data to answer problems 6 through 10.

6. The pooled, or combined, proportion is
a. 0.640
b. 0.644
c. 0.666
7. The test statistic is
a. 0.08
b. 0.644
c. 0.788
8. The p-value is
a. 0.2148
b. 0.4296
c. 0.7852
9. The critical value is
a. 1.96
b. 2.009
c. 2.021
10. The 95% confidence interval is
a. (–0.119, 0.279)
b. (–0.124, 0.284)
c. (–0.126, 0.286)

In a taste test using two colas, a random sample of 30 males and 30 females were selected. 18 males and 24 of the females chose brand A. A test is conducted to determine if the population proportion of females for brand A is greater than the population proportion for males. Use this data for questions 11 through 14.

11. The test statistic is
a. 0.20
b. 1.69
c. 1.73
12. The p-value is
a. 0.0455
b. 0.0910
c. 0.9545
13. Is there evidence of a greater proportion at the α = 0.05 level?
a. no
b. yes
c. it cannot be determined
14. A 90% confidence interval is constructed to estimate the difference of the population proportion of females for brand A minus the population proportion of males for brand A. The lower bound of the confidence interval is
a. 0.010
b. 0.200
c. 0.390

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