A manufacturer wants to increase the shelf life of a line of cake mixes. Past re

Question

A manufacturer wants to increase the shelf life of a line of cake mixes. Past records indicate that the average shelf life of the mix is 216 days. After a revised mix has been developed, a sample of nine boxes of cake mix had a mean of 217.22 days with a standard deviation of 1.20 days.

Answer the following:

a. Assume you are trying to determine if the shelf life has increased. Determine if the appropriate hypothesis test should be an upper tail, lower tail, or 2-tail test.

b. Determine the value of the test statistic.

c. Determine the critical z or t value using a level of significance of 2.5%.

d. Determine the p-value.

e. State your conclusion: Reject Ho or Do not Reject Ho? (Using a significance level of 2.5%).

f. What is the probability of making a type I Error?

Explanation / Answer

(a) Upper tailed test

Data:   

n = 9    

= 216    

s = 1.2    

x-bar = 217.22    

Hypotheses:     

Ho: 216    

Ha: > 216    

(b) SE = s/n = 1.2/9 = 0.4   

t = (x-bar - )/SE = (217.22 - 216)/0.4 = 3.05

(c) = 0.025

Degrees of freedom = 9 - 1 = 8   

Critical t- score = 2.306004133    

Reject Ho if t > 2.306004133

(d) p- value = 0.007910518

(e) Decision (in terms of the hypotheses):     

Since 3.05 > 2.306004133 we reject Ho and accept Ha

Conclusion (in terms of the problem):

There is sufficient evidence that > 216 days

(f) 0.008

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