Problem

Test the claim about the population mean $\mu$ at the level of significance $\alpha$. Assume the population is normally distributed. Claim: $\mu<4715 ; \alpha=0.02$ Sample statistics: $\bar{x}=4917, s=5501, n=54$ What are the null and altemative hypotheses? \[ \begin{array}{l} \mathrm{H}_{0}: \nabla \nabla \\ \mathrm{H}_{\mathrm{a}}: \nabla \nabla \nabla \end{array} \] (Type integers or decimals. Do not round.)

Solution

Step 1 :The null hypothesis (H0) is always a statement of no effect or no difference. In this case, it would be that the population mean is equal to the claimed value.

Step 2 :The alternative hypothesis (Ha) is what we are testing for. In this case, it would be that the population mean is less than the claimed value.

Step 3 :So, the null and alternative hypotheses would be: H0: μ = 4715, Ha: μ < 4715

Step 4 :Final Answer: \(\boxed{H_{0}: \mu = 4715, H_{a}: \mu < 4715}\)

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