22 A simple random sample of size n= 200 drivers with a valid driver's license is asked if they drive an American-made automobile. Of the 200 drivers surveyed, 118 responded that they drive anAmerican-made automobile. Determine if a majority of those with a valid driver's license drive an American-made automobile at the a =0.05 level of significance......Calculate the test statistic.Test statistic =(Round to two decimal places as needed.)Calculate the P-value.P-value =(Round to three decimal places as needed.)State the conclusion for the test.Ho. Theresufficient evidence at the a =0.05 level of significance to conclude thatof all drivers with a valid driver's license drive an American-madeautomobile.

Solution: Given information: n= 200 Sample size of drivers x= 118 drivers drive American made automobile. p^=xn=118200=0.59 Sample proportion of drivers drive American made automobile. p= 0.50 Population proportion of drivers drive American made automobile. α=0.05 Level of significance To test the hypothesis Ho:p=0.50 VS Ha:p>0.50 Test statistic z =p^-pp×(1-p)nz =0.59-0.500.50×0.50200z =0.59-0.500.25200z =0.59-0.500.00125z =0.090.035355=2.5456z= 2.55 Test statistic z = 2.55 To find p value p value = P( Z> 2.55) p value = 1- P(Z< 2.55) p value = 1- 0.99461 From Z table p value = 0.00539 p value = 0.005 The p value for the test is 0.005 Decision: Reject Ho since p value is less than significance level. ( P value < α=0.05) Conclusion: Reject Ho. There is sufficient evidence at the α=0.05 level of significance to conclude that majority of all drivers with valid driver's licence drive an American made automobile.