Question

A carpenter is making doors that are 2058 millimeters tall. If the doors are too long they must be trimmed, and if they are too short they cannot be used. A sample of 5 doors is made, and it is found that they have a mean of 2047 millimeters with a standard deviation of 10 . Is there evidence at the 0.05 level that the doors are too short and unusable? State the null and alternative hypotheses for the above scenario.

Answer 1

Solution :

Given that,

Population mean = = 2058

Sample mean = = 2047

Sample standard deviation = s = 10

Sample size = n = 5

Level of significance = = 0.05

This is a left (One) tailed test,

The null and alternative hypothesis is,  

Ho: 2058

Ha: 2058

The test statistics,

t = ( - )/ (s/)

= ( 2047 - 2058 ) / ( 10 / 5)

= -2.460

df = n - 1 = 4

P- Value = 0.0349   

The p-value is p = 0.0349 < 0.05,  it is concluded that the null hypothesis is rejected.

Conclusion :

It is concluded that the null hypothesis Ho is rejected. Therefore, there is enough evidence to claim that the doors are too

short and unusable , at the 0.05 significance level.