# Perform a hypothesis testing for one mean using t distribution

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.

a) At the 0.05 significance level, what is the critical value?

b) State the null and alternative hypothesis.

c) Draw a diagram.

d) Provide the computation of the test statistic.

e) State your decision in terms of the null hypothesis.

f) That is show the 5 steps of hypothesis testing

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#### Solution Preview

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a) At the 0.05 significance level, what is the critical value?

At the 0.05 level with degrees of freedom=9-1=8, the critical value is 1.86

b) State the null and alternative hypothesis.

Let u be mean shelf life of a line of cake mixes. So null hypothesis is u=116 and alternative hypothesis is u>116 ...

#### Solution Summary

The solution gives detailed steps on performing a hypothesis testing for one mean using t distribution.