Question

Question One

The manufacturer of a new car claims for it an average mileage of 60 km per litre with a standard deviation of 2 km under city conditions. However, the mileage in 64 trials is found to be 57 km.

Test to determine if the manufacturer’s claim is justified at 5% level of significance.                                                                                                                                                (6 marks)

i)                                  Construct the 99% confidence interval estimate for the mean mileage            (2 marks)

Answer 1

$H_0:\mu=60$ , average mileage is 60 km

$H_a:\mu\neq60$ , average mileage is not 60 km

$t=\frac{\overline{x}-\mu}{\sigma/\sqrt n}=\frac{57-60}{2/8}=-12$

$df=n-1=63$

critical value:

$t_{crit}=2$

Since  $|t|>t_{crit}$ , we reject the null hypothesis. Average mileage is not 60 km

 for 99% confidence interval:

$t_{crit}=\pm 2.66$

$-2.66<\frac{57-\mu}{2/8}<2.66$

$-0.665<57-\mu<0.665$

$56.335<\mu<57.665$