Question

A carpenter is making doors that are 20582058 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 3333 doors is taken, and it is found that they have a mean of 20682068 millimeters. Assume a population standard deviation of 2020. Is there evidence at the 0.020.02 level that the doors are either too long or too short?

Find the P-value for the hypothesis test. Round your answer to four decimal places. State the null and alternative hypotheses. Make the decision to fail or reject the null hypothesis

Answer 1

Solution :

The null and alternative hypothesis is ,

H₀ :   = 2058

H_a : > 2058

= 2068

= 20

n = 33

This is the right tailed test .

Test statistic = z =

= ( - ) / / n

= (2068 - 2058) / 20 / 33

Test statistic = z = 2.87

p(Z > 2.87) = 1-P (Z < 2.87) = 1 - 0.9979

P-value = 0.0021

= 0.02  

P-value <

Reject the null hypothesis .