Question

A lumber company is making boards that are 2906.0 millimeters tall. If the boards are too long they must be trimmed, and if the boards are too short they cannot be used. A sample of 12is made, and it is found that they have a mean of 2908.7 millimeters with a standard deviation of 11.0 A level of significance of 0.1 will be used to determine if the boards are either too long or too short. Assume the population distribution is approximately normal. Find the value of the test statistic. Round your answer to three decimal places.

Answer 1

Solution :

Given that,

Population mean = = 2906

Sample mean = = 2908.7

Sample standard deviation = s = 11

Sample size = n = 12

Level of significance = = 0.1

The null and alternative hypothesis is,

This a right (One) tailed test.

Ho: 2906

Ha: 2906

The test statistics,

t = ( - )/ (s/)

= ( 2908.7 - 2906 ) / ( 11/12)

= 0.850

p-value = 0.2066 ( using probability t- distribution table)

The p-value is p = 0.2066 > 0.1 it is concluded that the null hypothesis is fails to reject.

Conclusion:

There is not enough evidence to claim that , the company is making boards that are 2906.0 millimeters tall . at 0.1 level of

significance.