A sample of 286 urban adult residents of a particular state revealed 63 who favo
ID: 3172035 • Letter: A
Question
A sample of 286 urban adult residents of a particular state revealed 63 who favored increasing the highway speed limit from 55 to 65 mph, whereas a sample of 179rural residents yielded 79 who favored the increase.
A sample of 286 urban adult residents of a particular state revealed 63 who favored increasing the highway speed limit from 55 to 65 mph, whereas a sample of 179 rural residents yielded 79 who favored the increase. (a) Calculate the point estimate and margin of error for a 95% confidence interval for the difference in parameters p1 p2, where p1 refers to the true proportion of the urban population that favors increasing the speed limit and p2 refers to the true proportion ofthe rural population that favors increasing the speed limit. (Round your answers to two decimal places.) Estimate Margin of Error b) Does this data indicate that the sentiment for increasing the speed limit is different for the two groups of residents? Test Ho: p1 0 versus P2 Ha: p1 p2 t 0 using a 0.05. (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. 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 Fail to reject Ho. The data suggests that the sentiment for increasing the speed limit is different for the two groups of residents. 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.Explanation / Answer
a. The point estimate for difference in true proportion of two populations is the difference of their sample proportions.
Estimate:p1-p2, where p1 and p2 denotes population proportion of adult urban and rural residents who favoured increasing highway speed.
=p1hat-p2hat, phat denotes sample proportion.
=63/286-79/179
=-0.22
Margin of error: zalpha/2 sqrt[p1hat(1-p1hat)/n1+p2hat(1-p2hat)/n2], where, z denotes z critical at alpha/2, p1hat is sample proportion denoting urban adult residents, p2hat is sample proportion for rural adult residents, n1 and n2 denotes respective sample sizes.
=1.96 sqrt[63/286(1-63/286)/286+79/179(1-79/179)/179]
=1.31
b. Compute the pooled sample proportion, phatp=(x1+x2)/(n1+n2), where, x denotes number of events and n denotes number of trials, 1 and 2 denote population 1 and populaion 2 respectively.
phatp=(63+79)/(286+179)
=0.3054
z=(p1hat-p2hat)/[sqrt {phatp(1-phatp)} sqrt(1/n1+1/n2)]
=(63/286-79/179)/[sqrt{0.3054(1-0.3054)} sqrt{1/286+1/179}]
=-5.04
p value: 0.0000
Per rule reject H0, if p value is less than alpha=0.05. Here, p value is less than 0.05, therefore, reject H0 and conclude that there is significant difference in the sentiment for increasing speed for urban adult residents and rural adult residents.
Option 4.