Question

please help

of 480 drivers from the South, 402 weat a seatbelt in a survey 380 drivers from the Northeast, 290 wear a seatbelt. At Q =0.de, can you support the claim that the proportion of dovers who wear seatbelts is greater in the South than in the Northeast. Assume the random Samples are independante complete parts a throuel. Che Identify the claim b. Find the critical values and identify the rejection region c. Find the standardized test statistic Decide whether to fail or fail to reject null hypother le. Interpret the decision

Answer 1

Ho: pl < p2 H1: pl > p2 a.) claim :

Proportion of drivers who wear seatbelt is greater in the south than in the Northeast.

b.)

Critical value Za/2) = 1.55 use standard normal table

Rejection Region: Any test statistic value greater than 1.55

$\\\\ c.)\\ \hat{p1}=\frac{x1}{n1}=\frac{402}{480}=0.8375\\\\ \hat{p2}=\frac{x2}{n2}=\frac{290}{380}=0.7632\\\\ \hat{p}=\frac{x1+x2}{n1+n2}=\frac{402+290}{480+380}=0.8047\\\\ Test~Statistic(Z)=\frac{\hat{p1}-\hat{p2}}{\sqrt{\hat{p}*(1-\hat{p})*(\frac{1}{n1}+\frac{1}{n2})}}=\frac{0.8375-0.7632}{\sqrt{0.8047*(1-0.8047)*(\frac{1}{480}+\frac{1}{380})}}\\\\ \\ Z=2.73\\\\ d.)P-value=P(Z>2.73)\\\\ =1-P(Z \leq 2.73)\\\\ =1-0.9968\\\\ (use~z~table)\\\\ =0.0032\\\\ as~p-value~is ~less~than~\alpha=0.06\\\\ Reject~the~Null~hypothesis.$

e.)There is enough evidence to support the claim that Proportion of drivers who wear seatbelt is greater in the south than in the Northeast.