Conduct a one-tailed hypothesis test given the information below.
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 116 days. After a revised mix has been developed, a sample of nine boxes of cake mix had a mean of 117.333 and a standard deviation of 2.456. At the 0.05 significance level, what is the critical value? State the null and alternative hypothesis. Draw a diagram. Provide the computation of the test statistic. State your decision in terms of the null hypothesis.