Question

A sample of 35 cars of a certain kind had an average mileage of 36.2 mpg. Assuming that mileage is approximately normally distributed with standard deviation 4 mpg, test the hypothesis that the average mileage for all cars of this type is no less than 34.2 mpg at the 0.01 significance level. Give the value of p you find to two decimal places, and choose the correct conclusion:

p=

Answer 1

Solution:

H0 :   34.2  

H1 :   > 34.2

n = 35

= 36.2

= 4

Use = 0.01

The test statistic z is given by

z =

= (36.2 - 34.2) / (4/35)

= 2.96

Now , observe that ,there is > sign in H1. So , the test is right tailed.

p value = P(Z > 2.96)

= P(Z < -2.96)

= 0.0015 (use z table)

= 0.00 (up to two decimals)

p value is less than = 0.01

So , reject the null hypothesis H0.

We can conclude that there is sufficient evidence to support the claim that "mean is no less than 34.2"