Question

A machine is supposed to fill bags with an average of 19.2 oz of candy. The manager of the candy factory wants to be sure that the machine does not consistently underfill or overfill the bags. The manager takes a random sample of 35 bags of candy produced that day and weighs each bag. The average weight of these bags is 20 oz with a standard deviation of 3 oz. At α = 0.1, is there enough evidence to support the claim that the machine overfills the bags? Please show work.

Answer 1

Solution:

This a right (One) tailed test.

The null and alternative hypothesis is,  

Ho: 19.2

Ha: 19.2

The test statistics,

t =( - )/ (s /n)

= ( 20 - 19.2 ) / ( 3 / 35 )

= 1.578

P-value = 0.0619

The p-value is p = 0.0619 < 0.1, it is concluded that the null hypothesis is rejected.

There is enough evidence to support the claim that the machine overfills the bags.