Suppose you work for a university. You are tasked with studying the salaries that your graduating students make after five years. To do this, you randomly sample 150 students that graduated with a B.A. five years ago and sample 70 students that graduated with a B.S. five years ago. You contact all of them and ask them to report their current salary. If someone is currently unemployed or between jobs, you don't record anything. After tabulating the data, you find 20 people with B.A.'s responded and 19 people with B.S.'s responded. You get the following data (all salaries in thousands of dollars per year).
Graduated with B.A.:
34,43,48,50,51,54,62,63,65,67,67,70,70,72,75,79,81,84,88,92
Graduated with B.S:
42,54,58,62,63,67,72,74,75,75,80,82,83,83,84,87,90,94,94
(a) Test at @ = .05 to see if the University can claim that students who graduate with a B.S. from their university will make more on average in five years that students who graduate with a B.A. from their University. Make sure to confirm all necessary conditions and state your conclusion in the context of the problem.
(a) with this new data point. Did anything change? would you trust these new results? why or why not?
(b) Build a 95% confience interval for the average difference in salary after five years that graduates with a B.S. will make compared to graduates with a B.A.. Make sure to interpret your interval.
(c) Combining the two samples together, test at @= .05 to see if the University can claim that students who graduate from their university will have an average salary above $68,000 in five years. Make sure to confirm all necessary conditions and state your conclusion in the context of the problem.
(d) Explain what it would mean to make a Type I error in this situation. Then explain what it would mean to make a Type II error in this situation.
(e) Build a 95% confience interval for the average salary after five years that graduates from your University make. Make sure to interpret your interval.
(f) Look back at how the data was collected. Describe two flaws or biases with this approach.
(g) Suppose that a person calls you back and reports that they miswrote their salary. Instead of $34,000, they meant $340,000.