A Packaging Company produces boxes out of cardboard and has a specified weight o

Question

A Packaging Company produces boxes out of cardboard and has a specified weight of 30 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 30.5 oz. At 5% level of significance, test the claim that the mean weight of a box is 30 oz or is there significant evidence that the mean weight is not equal to 30 oz. Clearly state the null hypothesis, the alternative hypothesis, the test statistic, the critical value, the p-value and the decision and interpretation (significance statement).

Explanation / Answer

Ho: Mu = 30

Ha: Mu!= 30

Test statistic = Z = (30.5-30)/(1.3/sqrt(36)) = 2.31

The p value is 1-.9896 = .0104

Critical value is 1.96

So, Z=2.31>1.96 and hence the H0 is rejected

The conclusion is Ha: Mu!= 30

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