Question

An automobile manufacturer has given its jeep a 56.7 miles/gallon (MPG) rating. An independent testing firm has been contracted to test the actual MPG for this jeep since it is believed that the jeep has an incorrect manufacturer's MPG rating. After testing 160 jeeps, they found a mean MPG of 56.4. Assume the population variance is known to be 4.41. A level of significance of 0.05 will be used. State the null and alternative hypotheses.

Answer 1

1) Hypothesis :

H0 : = 56.7

H1: 56.7

Given

X_bar =56.4

n = 160

2 = 4.41

= sqrt (4.41) = 2.1

2) Test statistic Z value

z = (x_bar - ​​​​​​) /(/sqrt (n))

= (56.4/56.7)/(2.21/sqrt (160)

z = - 1.72

3) P value for Z test statistic is 0.086

P value = 0.086

4) conclusion:

P value (0.086) Is greater than 0.05 level of significance hence fail to reject null hypothesis. Therefore there is not enough evidence to claim the population mean different than 56.7.