### Question Description

I don’t understand this Statistics question and need help to study.

1. The mean salary of federal government employees on the General Schedule is $59,593. The average salary of 30 state employees who do similar work is $58,800 with σ= $1500. At the 0.01 level of significance, can it be concluded that state employees earn on average less than federal employees? Show all of your steps.

2. 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 α= 0.05, is there sufficient evidence that state senators are on average younger than the Senators in Washington? Also state the p-value of the test statistic. Show all of your steps.

3. Find the p-value, using the following information. The test statistic in a left-tailed test is z = -1.25.

4. Find the p-value, using the following information. The test statistic in a two-tailed test is z = 1.75.

5. Find the p-value, using the following information. Alternative hypothesis: , the test statistic is z = -3.35.

6. Find the p-value, using the following information. Alternative hypothesis: p > 1/4, the test statistic is z = 2.30.

7. Let the p-value be equal to 0.045. Use a 0.05 significance level to reject or fail to reject the null hypothesis.

8. Let the p-value be equal to 0.045. Use a 0.01 significance level to reject or fail to reject the null hypothesis.

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