Question

Beer shelf life is a problem for brewers and distributors because when beer is stored at room temperature, its flavor deteriorates. When the average furfuryl ether content reaches 6 μg per liter, a typical consumer begins to taste an unpleasant chemical flavor. At α = .05, would the following sample of 12 randomly chosen bottles stored for a month convince you that the mean furfuryl ether content exceeds the taste threshold?

7.21 7.03 7.04 5.17 5.18 7.97 5.83 5.56 6.88 7.48 6.00 7.07

a) For the following hypothesis H0: μ ≤ 6 versus H1: μ > 6, what is the value of the test statistic?

b)What is the p-value?

Answer 1

For testing the hypthesis we first have to calculate the mean and standard devition for this sample

Mx= 78.42/12= 6.54

s= 9.7466/11= 0.94

a) The following null and alternative hypotheses need to be tested:

Ho: μ ≤ 6

Ha: μ > 6

This corresponds to a right-tailed test

= 1.796 (from t-table at 95% confidence level and DF=12-1=11)

The rejection region for this right-tailed test is R=t:t>1.796

The t-test is calculated as

t=1.99

b) The p-value is p=0.036 (at 95% confidece leveland DF=11)

and since p=0.036<0.05, it is concluded that the null hypothesis is rejected. Hence there is enough evidence to claim that μ > 6.