Question

HT Mean: A Packaging Company produces boxes out of cardboard and has a specified weight of 35 oz. It is known that the weight of a box is normally distributed with standard deviation 1.3 oz. A random sample of 36 boxes yielded a sample mean of 35.5 oz. At 5% level of significance, test the claim that the mean weight of a box is 35 oz or is there significant evidence that the mean weight is greater than 35 oz. Determine the p-value to four decimal places.

Answer 1

Null and alternative hypotheses

Ho : = 35

H1 : > 35

Test statistic

Z = ( xbar - )/(/√n)

Z = ( 35.5 - 35)/(1.3/√36)

Z = 2.31

Zcritical for a = 0.05 and right tailed test

Zcritical = Z​​​​​​1-a​​​ = Z​​​​​​0.95 = 1.645

Decision rule : if Z > 1.645 we reject the null hypothesis otherwise we fail to reject the null hypothesis

Our Z = 2.31 > 1.645

Decision : we reject the null hypothesis

There is sufficient evidence to support the claim that the mean weight of box is greater than 35 Oz

p-value = P( Z > 2.31)

Using Z table

p-value = 0.0104