SAMPLE PROBLEM 5B--MALE AND FEMALE VOTING--PROPORTIONS
1. Use spreadsheet < Z12PROPS > to conduct estimation and hypothesis testing on the population proportions of males and females that may vote for a particular candidate in an upcoming election. Two polls were conducted with the following results:
Sample
Size “X” value
Males (X) 500 230
Females (Y) 400 210
a. The point estimate of the population proportion is:
Males: 0.46 Females: 0.525
b. The sampling standard deviation (standard error) of the sample proportions is:
Males: 0.0222890 Females: 0.0249687
c. The 99% confidence interval for the population proportion is:
(use point estimate ± error factor format, not LCL and UCL)
Males: πx = 0.46 ± 0.0574128 Females: πy = 0.525 ± 0.0643153
d. What sample size is needed for an error factor "E" of ± 0.03 at the 99% confidence level?
Males: 1832 Females: 1839
Test the H0 that each population proportion is 0.5 against the Ha that it is not 0.5.
e. State the H0:
Males: πx = 0.5 Females: πy = 0.5
f. State the Ha:
Males: πx ≠ 0.5 Females: πy ≠ 0.5
g. Use α = 0.10. State the zt, table-z, or critical value:
Males: zt = ± 1.645 Females: zt = ± 1.645
h. The zc, calculatedz or test statistic is:
Males: zc = - 1.788854 Females: zc = 1.000000
i. The hypothesis-test conclusion is:
Males: H0 is rejected. * Females: H0 is not rejected. **
* The difference between the sample proportion, 0.46, and the null hypothesis, 0.5, is statistically significant at the 0.10 level. The population proportion is probably not 0.5.
** The difference between the sample proportion, 0.525, and the null hypothesis, 0.5, is not statistically significant at the 0.10 level. The population proportion could be 0.5.
j. What is the pvalue in this test?
Males: 0.0736382 Females: 0.317311
2. Using the same data, conduct estimation and hypothesis testing on the difference between population proportions of males and females.
a. The point estimate of the difference between population proportions is:
- 0.065
b. The sampling standard deviation (standard error) of the differences between sample proportions is:
0.0334699
c. The 95% confidence interval for the difference between population proportions is
(use point estimate ± error factor format, not LCL and UCL)
(π1 - π2) = - 0.065 ± 0.0655998
d. What sample size is needed for an error factor "E" of ± 0.04?
1196
Test the H0 that the population proportions are equal against the Ha that they are not equal.
e. State the H0: (π1 - π2) = 0
f. State the Ha: (π1 - π2) ≠ 0
g. Use α = 0.05. State the zt, table-z, or critical value: ± 1.960
h. The zc, calculatedz or test statistic is: - 1.938404
i. The hypothesis-test conclusion is: H0 is not rejected. *
* The difference between the sample proportions, 0.065, is not statistically significant at the 0.05 level. The population proportions could be equal. (However, the null hypothesis was nearly rejected. It is possible that slightly larger samples would have provided a rejection of the null hypothesis.)
j. What is the pvalue in this test? 0.0525738