Question

A recruiting firm report on starting salaries states that starting salaries for finance majors are skewed to the right, with a nationwide mean of $58,993.

a. We collect starting salary data from a random sample of 50 recently graduated finance
majors from a well- regarded business program at a large state university. Why is it okay to use these data for inference even though the population is skewed?

b. The standard deviation of the 50 salaries in our sample was $11,717. Specify the sampling model (shape, center, spread) for the mean price of such samples.

c. This sample of randomly chosen salaries produced a 90% confidence interval for the mean starting salary for finance majors from this business program ($59347, $64903). Does this interval provide evidence that starting salaries are unusually high for graduates from the
business program at this university? Explain briefly.

d. Suppose we hope improve our estimate by choosing a new sample. How many starting salaries must we survey to have 90% confidence of estimating the mean starting salary to within $1000?

Answer 1

a)We are trying to find out what is the mean average salary from the population. The shape of the actual distribution doesnot impact the mean of the sampling distribution. This is as per the central limit theorem.

b)The sampling model for the mean is expected to be a normal distribution with mean=58993 and spread=11717/sqrt(50)=1657

Yes the interval shows a higher starting salary than the one calculated. The mean is expected to follow a confidence interval calculated above. A higher interval could prove multiple things, one either the sample is not random or second there is a huge type 1 error.

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