Question

The FMA Company has designed a new type of 16 lb. bowling ball. The company knows that the average man who bowls in a scratch league with the company's old ball has a bowling average of 155. The company asks a random sample of 120 men bowling in scratch leagues to bowl for five weeks with their new ball. The mean of bowling averages for these men with the new ball is 170. The variance is 100. If we want to test the null hypothesis that the new ball does not have the same bowler's average as the last ball using α=0.05, find the rejection region and test statistic of the necessary test to be held? Show all work.

Answer 1

Given

n = 120 , , ,

Null and alternative hypothesis is

H0 : u = 155

H1 : u ≠ 155

Level of significance = 0.05

Here population standard deviation is not known so we use t-test statistic.

Test statistic is

Test statistic is t = 16.43

Degrees of freedom = n - 1 = 120-1=119

P-value = 0.00001 ( using t table)

Rejection Region : P-value , Reject H0

Here ,P-value , Reject H0

conclusion : At α=0.05,the new ball does not have the same bowler's average as the last ball