The dean of the College of Business at the University 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 250 alumni and finds that the mean of their salary is $50k. Assuming a 95% confidence level, please do the following. Please show all steps in the process. I am learning this process as well. Thank you

1.Suppose the dean believes that the average salary of the population should be about $55k per year, with a standard deviation of $9k. We need to conclude that the mean salary is less than what the dean has believed to be (Hint: Hypothesis Testing and Confidence Interval - One sample; population standard deviation is known)

(a)What are the null and alternate hypotheses?

(b)What is the level of significance ?

(c)What is the standard error ?

(d)Decide on the test statistic and calculate the value of the test statistic (hint: write the equation and calculate the statistic)?

(e)What's your decision regarding the hypothesis and interpret the result using test-score rejection region rule or p value rule.

2.Suppose the population standard deviation of $9k: (Hint: Hypothesis Testing and Confidence Interval - One sample; population standard deviation is known)

(a)What is the Z critical value of 95% confidence interval?

(b)What is the standard error?

(c)Please estimate the confidence interval of the population's average salary (hint: write down the equation and calculate the results)