Question

Problem 2.22 (modified from Montgomery, 9th edition) The mean shelf life of a carbonated drink should exceed 120 days. Ten bottles are randomly selected and tested, and the results below are obtained: shelf life (days) = {108, 124, 124, 106, 115, 138, 163, 159, 134, 139} a) Clearly state the hypothesis to be tested, first in English and then in mathematical expressions for H0 and H1. b) Test the hypothesis at significance level 0.01. Report both the p-value and a 99% confidence interval to support your conclusion. Be sure to clearly state your conclusion in plain English and within the context of the problem.

Answer 1

Here Ten bottles are randomly selected and tested, and the results below are obtained: shelf life (days) = {108, 124, 124, 106, 115, 138, 163, 159, 134, 139}

So for this sample mean is

Create the following table.

data	data-mean	(data - mean)2
108	-23	529
124	-7	49
124	-7	49
106	-25	625
115	-16	256
138	7	49
163	32	1024
159	28	784
134	3	9
139	8	64

Find the sum of numbers in the last column to get.

So standard deviation is

a. Here claim is that mean shelf life of a carbonated drink should exceed 120 days.

So hypothesis is vs

b. As n=10<30, and population variance is not known, so we will use t distribution to find test statistics

Now P value for right tailed test is TDIST(tstat,df,1)=TDIST(1.78,9,1)=0.0544

As P value is greater than we fail to reject the null hypothesis

Now for 99% CI, t table value for 9 df is  3.250

So Margin of Error is

Hence CI is

As we see that mean range have value more than 120, hence we fail to reject the null hypothesis

Hence we have sufficient evidence to support the claim that mean is greater than 120

Hence we conclude that the mean shelf life of a carbonated drink exceed 120 days