Question

Prior to the deployment of the Iraqi Freedom military operation in March 2003, a sample of 510 telephone interviews was conducted by the Washington Post-ABC Poll to gauge the approval or disapproval of the war. In sum, 64% of those polled approved the way the president was handling the Iraqi situation. In October 2002, the same poll showed that the approval rating was 57%. Assuming the sample sizes were the same, using a 01 level of significance, test the hypothesis that the March 2003 rating and October 2002 rating are not significantly different. since 2.287,<2.5762, we can not reject the Null Hypothesis. There is insufficient evidence to conclude that the proportions in March 2003 and October 2002 are statistically different. since 2.287, > 2.576z, we can reject the Null Hypothesis. There is insufficient evidence to conclude that the proportions in March 2003 and October 2002 are statistically different. since 2.2872 > 2.576z, we can reject the Null Hypothesis. There is sufficient evidence to conclude that the proportions in March 2003 and October 2002 are statistically different. since 2.287,<2.5762, we can reject the Null Hypothesis. There is sufficient evidence to conclude that the proportions in March 2003 and October 2002 are statistically different. None of the answers is correct.

Answer 1

The statistical software output for this problem is:

Two sample proportion summary bypothesis test: Pproportion of successes for population 1 P2 proportion of successes for population 2 P.-P.: Difference in proportions HP-P, = 0 HAPP20 Hypothesis test results: Difference Countl Totall Count2 Total2 Sample Diff. Std. Err. Z-Stat P-value 326.4 510 290.7 510 0.07 0.030613018 2.2866089 0.0222

From above output:

Test statistic = 2.287

Critical value at 0.01 significance level = 2.576

Hence,

since 2.287,> 2.576z, we can reject the Null Hypothesis. There is sufficient evidence to conclude that the proportions in March 2003 and October 2002 are statistically different.

Option C is correct.