A government agency believes that the median hourly wages...

A government agency believes that the median hourly wages for retail store workers in a certain region of the country is $6.05. In a random sample of 100 workers, 68 were paid less than $6.05, 10 were paid $6.05, and the rest were paid more than $6.05. Find the critical values to test the government's hypothesis. Use α=0.05. Round to two decimal places.

Perform each of the following steps. a. State the hypotheses and identify the claim. b. Find the critical value(s). c. Compute the test value. d. Make the decision. e. Summarize the results. Use the traditional method of hypothesis testing unless otherwise specified. The average per capita income for Wisconsin is reported to be $\$ 37,314,$ and for South Dakota it is $\$ 37,375-$ almost the same thing. A random sample of 50 workers from each state indicated the following sample statistics. $$ \begin{array}{lll} & & \text { South } \\ & \text { Wisconsin } & \text { Dakota } \\ \hline \text { Size } & 50 & 50 \\ \text { Mean } & \$ 40,275 & \$ 38,750 \\ \text { Population standard deviation } & \$ 10,500 & \$ 12,500 \end{array} $$ At $\alpha=0.05,$ can we conclude a difference in means of the personal incomes?

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