Question

The manufacturer of a certain brand of pre-made hamburgers claims that the mean fat content of its burgers is 12 grams. Management is concerned that the true average fat content of the burgers is higher than this amount. To investigate, they sample 20 burgers and find a mean fat content of 13.1 grams. Assuming that the fat content of burgers is Normally distributed with a population standard deviation of ? = 3.1 grams, is there evidence that the true average fat content is more than 12 grams? Answer this question using a hypothesis test and alpha-level of 0.01.

Answer 1

Solution :

This is the two tailed test,  

The null and alternative hypothesis is ,

H0 :   = 12

Ha : > 12

Test statistic = z

= ( - ) / / n

= (13.1- 12) / 3.1 / 20

Test statistic = z = 1.59

P(Z > 1.59) = 1-P (Z < 1.59) = 1 - 0.9441

P-value = 0.0559

= 0.01

P-value >

Fail to reject the null hypothesis,

There is not sufficient evidence to suggest that the true average fat content is more than 12 grams