(Solved): Use a t-test to test the claim about the population mean at the given level of significance ...

Use a t-test to test the claim about the population mean $?$ at the given level of significance $?$ using the given sample statistics. Assume the population is normally distributed. Claim: $?=51,200;?=0.05$ Sample statistics: $\stackrel{?}{x}=50,179,s=2700,n=19$ Click the icon to view the t-distribution table. What are the null and alternative hypotheses? Choose the correct answer below. A. $\begin{array}{l}{H}_0:??51,200\\ H_a:?<51,200\end{array}$ c. $\begin{array}{l}{H}_0:??51,200\\ H_a:?>51,200\end{array}$ B. $\begin{array}{l}{H}_0:??=51,200\\ H_a:?=51,200\end{array}$ D. $\begin{array}{l}{H}_0:?=51,200\\ H_a:??=51,200\end{array}$ What is the value of the standardized test statistic? The standardized test statistic is (Round to two decimal places as needed.) What is(are) the critical value(s)? The critical value(s) is(are) (Round to three decimal places as needed. Use a comma to separate answers as needed.) Decide whether to reject or fail to reject the null hypothesis. A. Fail to reject ${\mathrm{H}}_0$. There is not enough evidence to reject the claim. B. Reject ${\mathrm{H}}_0$. There is not enough evidence to reject the claim. C. Reject ${\mathrm{H}}_0$. There is enough evidence to reject the claim. D. Fail to reject ${\mathrm{H}}_0$. There is enough evidence to reject the claim.