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 threshhold?

6.72	5.94	8.83	8.86	6.38	5.36	7.79	7.21	8.40	8.09	5.52	5.42

(a)	For the following hypothesis
	H0: μ ≤ 6 versus H1: μ > 6, what is the value of the test statistic? (Round your answer to 3 decimal places.)

Test statistic

(b)	What is the p-value? (Round your answer to 4 decimal places.)

p-value

(c)	At α = .05, we would
	reject the null hypothesis. fail to reject the null hypothesis.

Answer 1

	Values ( X )
	6.72	0.1045
	5.94	1.2173
	8.83	3.1923
	8.86	3.3004
	6.38	0.44
	5.36	2.8335
	7.79	0.5576
	7.21	0.0278
	8.4	1.8406
	8.09	1.0956
	5.52	2.3204
	5.4	2.6351
Total	84.52	19.5651

Test Statistic :-

t = 2.7098

Test Criteria :-

Reject null hypothesis if

Result :- Reject null hypothesis

P value

Looking for the value  t = 2.7098 in t table across 11 degree of freedom

t = 2.7098 lies between the values 2.201 and 2.718 respective P vlaues are 0.025 and 0.010.

Using excel to calculate P value = 0.0101

Decision based on P value

Reject null hypothesis if P value < level of significance

0.0101 < 0.05, reject null hypothesis

We would reject null hypothesis.