Question

The latest model of a certain brand of electric car is reported to have an average range of 195 miles. An auto industry journalist would like to verify this claim, since she believes that the true range of the car may be less than 195 miles. The journalist selected and tested a random sample of 80 cars of this model and found that the average range of the sample was 190.8 miles with a standard deviation of 31.3 miles. Apply the p-value method to test the hypothesis that the average range of this electric car model is less than 195 miles, using a significance level of 0.5%. State the null and alternative hypothesis for this test. H:27 H:27 Determine if this test is left-tailed, right-tailed, or two-tailed. Oright-tailed Otwo-tailed Oleft-tailed Should the standard normal (z) distribution or Student's (t) distribution be used for this test? The Student's t distribution should be used The standard normal (2) distribution should be used Determine the test statistic for the hypothesis test. Round the solution to four decimal places. Determine the p-value (range) for the hypothesis test. Op-value < 0.0005 0.0005 < p-value < 0.005 O 0.005 <p-value < 0.01 0.01 <p-value < 0.025 O 0.025 <p-value < 0.05 O 0.05 <p-value < 0.10 Op-value > 0.10 Determine the appropriate conclusion for this hypothesis test. The sample data do not provide sufficient evidence to reject the null hypothesis that the average range of this electric car is 195 miles and thus we conclude that the true range of the electric car is likely 195 miles. The sample data provide sufficient evidence to reject the alternative hypothesis that the average range of this electric car is less than 195 miles and thus we conclude that the true range of this electric car is likely 195 miles. The sample data provide sufficient evidence to reject the null hypothesis that the average range of this electric car is 195 miles and thus we conclude that the true range of the electric car is likely less than 195 miles. The sample data do not provide sufficient evidence to reject the alternative hypothesis that the average range of this electric car is less than 195 miles and thus we conclude that the true range of this electric car is likely less than 195 miles.

Answer 1

n=80 Girn that Sample size sample mean Sample std du t = 1908 3= 31.3 Ho: U=195 U L 195 > Since Altemative (Hij is left- tailed test, < type, this is Since o is unknown. ✓ The student's t distribution should be used Test statistics is t= X-4 sin 190.8-195 31.3/80 t= -1.2002 - 1.2002 V df =n-1= 79 v P-value = p [ tra L-).2002] 0.116824 try -1.2002 је P-value >o.10 / . the sample data do not provide sufficient evidence to Reject to & thus we conclude that tale rage is likely 195 miles first option is consect.