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 1010 doors is made, and it is found that they have a mean of 20462046 millimeters with a standard deviation of 1515. Is there evidence at the 0.050.05 level that the doors are too short and unusable

Answer 1

Z= 0.253

Z∝/2 = ± 1.96

Explanation:

Formulate the null and alternative hypotheses as

H0 : u1= u2 against Ha : u1≠ u2 This is a two sided test

Here ∝= 0.005

For alpha by 2 for a two tailed test Z∝/2 = ± 1.96

Standard deviation = s= 15

n= 10

The test statistic used here is

Z = x- x`/ s/√n

Z= 2058- 2046 / 15 / √10

Z= 0.253

Since the calculated value of Z= 0.253 falls in the critical region we reject the null hypothesis.

There is evidence at the 0.05 level that the doors are too short and unusable.