Question

According to a certain government agency for a large country, the proportion of fatal traffic accidents in the country in which the driver had a positive blood alcohol concentration (BAC) is 0.33. Suppose a random sample of 114 traffic fatalities in a certain region results in 48 that involved a positive BAC. Does the sample evidence suggest that the region has a higher proportion of traffic fatalities involving a positive BAC than the country at the a = 0.01 level of significance? Because npo (1 - Po) 10, the sample size is 5% of the population size, and the sample the requirements for testing the hypothesis satisfied. (Round to one decimal place as needed.) What are the null and alternative hypotheses? versus H: (Type integers or decimals. Do not round.) Find the test statistic, 20 Ho: 20 (Round to two decimal places as needed.) Find the P-value. P-value = (Round to three decimal places as needed.) Determine the conclusion for this hypothesis test. Choose the correct answer below. O A. Since P-value > a, do not reject the null hypothesis and conclude that there is not sufficient evidence that the region has a higher proportion of traffic fatalities involving a positive BAC than the country. B. Since P-value <a, do not reject the null hypothesis and conclude that there is not sufficient evidence that the region has a higher proportion of traffic fatalities involving a positive BAC than the country. C. Since P-value <a, reject the null hypothesis and conclude that there is sufficient evidence that the region has a higher proportion of traffic fatalities involving a positive BAC than the country. OD. Since P-value > a, reject the null hypothesis and conclude that there is sufficient evidence that the region has a higher proportion of traffic fatalities involving a positive BAC than the country.

Answer 1

Solution Given data n=114 x = 48 P = 48 8 = 0.4211 &=o.or Po = 0.33 Because NP. (1-po) = 114 X 0.33 X 0.67 np. (6 p.) 25.2 10 114 x 0.33 (1-0.33) consider 0.05N = 0.05 X 10ooo 0.05 N = 500 > i.e n<0.05N Because np. (1-P) = (25.2 E 1o the sample size is less than 5% of the population size, and Population size, and the sample can be the requirements for testing the easonably assumed to be random hypothesis are satisfied

null and alternative Now to state the Versus p = 0.33 Null hypothesis H. Alternative hypothesis H,: p > 0,33 This is "right-tailed" test. Now to find the test statistic, Zo : We know that The formula of test statistic, Zo is given by Zo= P. (1-P.) n 0.4211-0.33 Zo 0.33/1-0.33) 48 0.0911 Z.= 0.33x0.67 48 0.0911 Zo= 0.2211 48 0.091 Zo= 10.004606

0.0911 Zo= 0.0679 Zo= 1.34 Test statistic, Z. = 1.34 * Now to find the P-value P-value Plz>1.34) - 1-P (Z<1.34) = -0.9099 = 0.0901 P-value = 0.090 Decision P-value > 0.090 oool Therefore we do not reject the null hypothesis (Ho) Conclusion : Since: P-value >d, do not reject the null hypothesis and conclude that there is not sufficient evidence that the higher proportion of traffic fatalities involving BAC than the country. Therefore the cloption=A" is the correct answer region has a a Positive