Question

A company advertises that the mean diameter of pipes is 3 inches however, a consumer agency believes that the mean diameter of these pipes is larger. A random sample of N = 36 pipes is taken and it is found the the sample mean diameter is 3.15 inches with a sample standard deviation of S = .2 inches. Test this hypothesis at 95% significance level. Your conclusion is:

Fail to reject the null

Reject the null

Answer 1

Solution :

Given that,

Population mean = = 3

Sample mean = = 3.15

Sample standard deviation = s = 0.2

Sample size = n = 36

Level of significance = = 0.05

This is a left (One) tailed test,

The null and alternative hypothesis is,  

Ho: 3

Ha: 3

The test statistics,

t = ( - )/ (s/)

= ( 3.15 - 3 ) / ( 0.2 /36 )

= 4.5

P- Value = 0.000   

The p-value is p =0.00 < 0.05, it is concluded that the null hypothesis is rejected.

Reject the null hypothesis.