Bags of a certain brand of tortilla chips claim to have a ne

Bags of a certain brand of tortilla chips claim to have a net weight of 14 ounces. The net weights actually vary slightly from bag to bag and are normally distributed with mean ?. A representative of a consumer advocacy group wishes to see if there is any evidence that the mean net weight is less than advertised.

For this, the representative randomly selects 16 bags of this brand and determines the net weight of each. He finds the sample mean to be 13.82 and the sample standard deviation to be 0.24.

Use these data to perform an appropriate test of hypothesis at 5% significance level.

Please show all your work.

Solution

The test hypothesis:

Ho: ?=14 (i.e. null hypothesis)

Ha: ?<14 (i.e. alternative hypothesis)

The test statistic is

t=(xbar-?)/(s/vn)

=(13.82-14)/(0.24/sqrt(16))

=-3

The degree of freedom =n-1=16-1=15

It is a left-tailed test.

Given a=0.05, the critical value is t(0.05, df=15) =-1.75 (from student t table)

The rejection region is if t<-1.75, we reject the null hypothesis.

Since t=-3 is less than -1.75, we reject the null hypothesis.

So we can conclude that there is an evidence that the mean net weight is less than advertised.