use a t - test to test the claim about the population mean $ \mu $ at the given level of significance $ \alpha $ using the given sample statistics. assume the population is normally distributed. claim: $ \mu \geq 7800 ; \alpha = 0.05 $ sample statistics: $ \bar{x}=7500, s = 430, n = 24 $ what are the null and alternative hypotheses? a. $ \begin{array}{l} h_{0}: \mu = 7800 \\ h_{a}: \mu \
eq 7800 \end{array} $ b. $ \begin{array}{l} h_{0}: \mu \geq 7800 \\ h_{a}: \mu \lt 7800 \end{array} $ c. $ \begin{array}{l} h_{0}: \mu \leq 7800 \\ h_{a}: \mu \gt 7800 \end{array} $ d. $ \begin{array}{l} h_{0}: \mu \
eq 7800 \\ h_{a}: \mu = 7800 \end{array} $ what is the value of the standardized test statistic? the standardized test statistic is $ -3.42 $. (round to two decimal places as needed.) what is the p - value? $ p = 0.001 $ (round to three decimal places as needed.) decide whether to reject or fail to reject the null hypothesis. choose the correct answer below. a. fail to reject $ h_{0} $. at the $ 5 \% $ level of significance, there is not enough evidence to reject the claim. b. reject $ h_{0} $. at the $ 5 \% $ level of significance, there is not enough evidence to reject the claim. c. fail to reject $ h_{0} $. at the $ 5 \% $ level of significance, there is enough evidence to reject the claim. d. reject $ h_{0} $. at the $ 5 \% $ level of significance, there is enough evidence to reject the claim.

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# Brief Explanations:
When conducting a hypothesis test, we compare the P - value with the significance level $\alpha$. If $P-\text{value}<\alpha$, we reject the null hypothesis $H_0$. Here, $\alpha = 0.05$ and $P = 0.001$. Since $0.001<0.05$, we reject $H_0$.

# Answer:
D. Reject $H_{0}$. At the 5% level of significance, there is enough evidence to reject the claim.

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