Statistics homework help. ** **

**Question 1-5 (100 points): **The dean of the College of Business at the University of La Verne has observed for several years and found that the probability distribution of the salary of the alumni’s first job after graduation is normal. The college collected information from 144 alumni and finds that the mean of their salary is $58k. Assuming a 95% confidence level, please do the following

- Suppose the dean believes that the average salary of the population should be about $59k per year, with
**a standard deviation of $2k**. We need to conclude that the mean salary is less than what the dean has believed to be (30points, Review PPT Chapter 10).*(**Hint: Hypothesis Testing and Confidence Interval – One sample; population standard deviation is known)*

- What are the null and alternate hypotheses (5 points)?
- What is the level of significance (5 points)?
- What is the standard error (5points)?
- Decide on the test statistic and calculate the value of the test statistic (hint: write the equation and calculate the statistic) (10 points)?
- What’s your decision regarding the hypothesis and interpret the result using test-score rejection region rule or p value rule (5 points).

- Suppose the population standard deviation of $2k (20points, Review PPT Chapter 9):
*(**Hint: Hypothesis Testing and Confidence Interval – One sample; population standard deviation is known)*

- What is the Z critical value of 95% confidence interval (5 points)?
- What is the standard error (5points)?
- Please estimate the confidence interval of the population’s average salary (hint: write down the equation and calculate the results) (10 points)

- Suppose the standard deviation of the collected data from 144 alumni is $3k. Can we conclude that the true mean of alumni salary is different from $58k (20 points; Review PPT Chapter 10)?
*(**Hint: Hypothesis Testing and Confidence Interval – One sample; sample standard deviation is known)*

- What are the null and alternate hypotheses (5 points)?
- Decide on the test statistic and calculate the value of the test statistic (hint: write the equation and calculate the statistic, 10 points).
- Please make the conclusion (5 points).

- Suppose that the standard deviation of the collected data from 144 alumni is $3k and the mean is $58k, please estimate the confidence interval of the population’s average salary (10 points, Review PPT Chapter 9).
*(**Hint: Hypothesis Testing and Confidence Interval – One sample; sample standard deviation is known)*

- The dean wants to know whether there is salary difference between male and female alumni. He knows that the population standard deviation for male is $3k and for female is $4k. The sampled data show that the average salary for 121 male is $60k and the average salary for 100 female is $56k (20 points, Review PPT Chapter 11).
*(**Hint: Hypothesis Testing and Confidence Interval – two samples; population standard deviation is known)*

- What are the null and alternate hypotheses (5 points)?
- Decide on the test statistic and calculate the value of the test statistic (hint: write the equation and calculate the statistic) (10 points)?
- What’s your decision regarding the hypothesis and interpret the result using test-score rejection region rule or p value rule (5 points).