12. -10 points A sample of 322 urban adult residents of a particular state revea

Question

12. -10 points A sample of 322 urban adult residents of a particular state revealed 62 who favored increasing the highway speed limit from 55 to 65 mph, whereas a sample of 190 rural residents yielded 79 who favored the increase. Does this data indicate that the sentiment for increasing the speed limit is different for the two groups of residents? My NotesAsk Your (a) Test to: p1-P2 = 0 versus Ha: p1-p2+ 0 using ? = 0.05, where pi refers to the urban population. (Round your test statistic to two decimal places and your P-value to four decimal places.) P-value - State the conclusion in the problem context o Reject Ho. The data does not suggest that the sentiment for increasing the speed limit is different for the two groups of residents Fail to reject Ho. The data does not suggest that the sentiment for increasing the speed limit is different for the two groups of residents o Reject Ho. The data suggests that the sentiment for increasing the speed limit is different for the two groups of residents o Fail to reject Ho. The data suggests that the sentiment for increasing the speed limit is different for the two groups of residents (b) If the true proportions favoring the increase are actually p1 0.21 (urban) and p2 0.42 (rural), what is the probability that Ho will be rejected using a level 0.05 test with n1322, n2-190? (Round your answer to four decimal places.)

Explanation / Answer

Data given is:

Sample proportions, p1 = 62/322 = 0.193, p2 = 79/190 = 0.416

Sample sizes, n1 = 322, n2 = 190

Standard error, S = (p1*(1-p1)/n1 + p2*(1-p2)/n2)^0.5 = (0.193*(1-0.193)/322 + 0.416*(1-0.416)/190)^0.5 = 0.0419

Test statistic, z = (p1-p2)/S = (0.193-0.416)/0.0419 = -5.322

The p-value for this z-value is: p = approximately zero

Since p < 0.05, so we have to reject the null hypothesis.

Reject H0. The data suggests that the sentiment differs for the two groups.

(b)

In this case,

Standard error, S = (p1*(1-p1)/n1 + p2*(1-p2)/n2)^0.5 = (0.21*(1-0.21)/322 + 0.42*(1-0.42)/190)^0.5 = 0.0423

Test statistic, z = (p1-p2)/S = (0.21-0.42)/0.0423 = -4.96

The p-value for this z-value is: p = approximately zero

Since p < 0.05, so we have to reject the null hypothesis.

Reject H0. The data suggests that the sentiment differs for the two groups.

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