Question

This is question 13 from the book, on p. 436. The numbers are probably no longer accurate, but don't worry about that.) Show all five steps of the hypothesis test. You can either type them in here, or write them out on paper and send me a scan/picture of your work.The mean age of Senators in the 209th Congress was 60.35 years. A random sample of 40 senators from various state senates had an average age of 55.4 years, and the population standard deviation is 6.5 years. At α = 0.05, is there sufficient evidence that state senators are on average younger than 60.35 (the average age Senators in Washington)?

Answer 1

There is not sufficient evidence to support the conclusion that senators are average younger than 60.35

Explanation:

Given a simple random sample, the size is 40 senators.

Since the relevant statistic is the sample mean, 60.35 years.

Calculate t as:

`t=\frac{\bar{x}-\mu_{\bar{x}}}{\frac{s}{\sqrt[]{n}}}`

*Significance level is 0.05.

`\begin{gathered} t=\frac{60.35-55.4}{\frac{6.5}{\sqrt[]{40}}} \\ t=4.82 \end{gathered}`

Area of 0.05, one-tail yields t=1.685.

Since t=4.82 does not fall in the critical region bounded, we fail to reject the null hypothesis.

There is not sufficient evidence to support the conclusion that senators are average younger than 60.35