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The dean of the school has observed for several years and found that the probability distribution...

The dean of the school 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:

1. Suppose the population standard deviation of $2k:

(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)

2. 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?

(a) What are the null and alternate hypotheses ?

(b) Decide on the test statistic and calculate the value of the test statistic.

(c) Please make the conclusion .

Math   Statistics-And-Probability   
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