Question

The mean age of Senators in the 109th 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 a 0.05 level of significance, is there sufficient evidence that state senators are on average younger than the Senators in Washington?

Answer 1

Perform a hypothesis test to determine if state senators are younger than Senators in Washington. Ater the test it is found that there is sufficient evidence to suggest that state senators are on average younger than the Senators in Washington.

Step-by-step explanation:

To determine if there is sufficient evidence that state senators are on average younger than the Senators in Washington, we can perform a hypothesis test.

Null hypothesis: The average age of state senators is equal to the average age of Senators in Washington.

Alternate hypothesis: The average age of state senators is younger than the average age of Senators in Washington.

Using a one-sample t-test with a significance level of 0.05, we can calculate the test statistic and compare it to the critical value from the t-distribution.

Let's perform the hypothesis test:

1. Calculate the test statistic:
2. t = (sample mean - population mean) / (population standard deviation / sqrt(sample size))
3. t = (55.4 - 60.35) / (6.5 / sqrt(40))
4. t = -4.95
5. Find the critical value from the t-distribution table for a one-tailed test at a significance level of 0.05 with 39 degrees of freedom: t-critical = -1.685
6. Compare the test statistic to the critical value. Since the test statistic (-4.95) is less than the critical value (-1.685), we reject the null hypothesis.
7. Therefore, there is sufficient evidence to suggest that state senators are on average younger than the Senators in Washington.