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# Perform a hypothesis testing for single mean using t distribution

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Willco is a manufacturer in a mature cyclical industry. During the most recent industry cycle, its net income averaged \$30 million per year with a standard deviation of \$10 million (n = 6 observations). Management claims that Willco's performance during the most recent cycle results from new approaches and that we can dismiss profitability expectations based on its average or normalized earnings of \$24 million per year in prior cycles.

A. With µ as the population value of mean annual net income, formulate null and alternative hypotheses consistent with testing Willco management's claim.
B. Assuming that Willco's net income is at least approximately normally distributed, identify the appropriate test statistic.
C. Identify the rejection point or points at the 0.05 level of significance for the hypothesis tested in part A.
D. Determine whether or not to reject the null hypothesis at the 0.05 significance level.

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The solution gives details steps on performing a hypothesis testing for single mean using t distribution.

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A. With µ as the population value of mean annual net income, formulate null and alternative hypotheses consistent with testing Willco management's claim.
null hypotheses: u=24
alternative hypotheses: u>24

B. Assuming ...

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