Question

The Mill Valley Brewery produces 32 ounce bottles of beer. The Bureau of Weights and Measures randomly selects 50 of these bottles, measures their contents, and obtains a sample mean of 31.8 oz and a sample standard deviation of 0.75 oz. At the 5% level, is there evidence that Mill Valley Brewery is cheating customers by under-filling their bottles?

Answer 1

Since the calculated Z= -1.886 lies within the Z∝ = ± 1.96 we fail to reject our null hypothesis that population mean is 31.8 oz. and not 32 ounces. There is evidence that Mill Valley Brewery is cheating customers by under-filling their bottles.

Explanation:

Let the null hypothesis be

H0 : u = 31.8 oz against Ha: u ≠ 31.8 oz two tailed test

For a two tailed test and alpha = 0.05 the z∝ = ± 1.96

The rejection region is Z ≥ ± 1.96

Here n = 50

sample mean = x= 31.8 oz

and sample standard deviation= s= 0.75

Population mean= u= 32

Test statistics to be used is

Z= x- u / s/ √n which is approximately normal

Z= 31.8-32/0.75/ √50

z= -1.886

Since the calculated Z= -1.886 lies within the Z∝ = ± 1.96 we fail to reject our null hypothesis that population mean is 31.8 oz. and not 32 ounces. There is evidence that Mill Valley Brewery is cheating customers by under-filling their bottles.