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1. Problem Name: "Purple Aces" Binomial Distribution (12 points)
a. You are an admission counselor, after a student's private visit there is a 45°0 chance the student will decide to apply to the University. You had 12 students visit last week. What are the chances that 7 students will apply,?
b. With the addition of a new academic center on campus, you now feel the probability of a student applying is at 50%. What are the chances that 6 or more students apply out of the total of 12?
c. A senior business graduate at UE is in the final stage of the interviewing process at five companies. The student assesses there is a 33% chance of being hired by any single company. What are the chances the student will get at least one offer?
2. Problem Name: "McGuires" Expected Value (4 points) Calculate the expected value of the investment below Investments
Profit Probability
15,000 0.2
10,000 0.45
4,000 0.25
-2,000 0.1
3. Hypothesis Testing: Tires are designed to last at least 45,000 miles. A sample of 100 tires shows tire life was ( ) -44,500 miles, and s 2,000 miles. Test at alpha = .01 to see if tires are lasting under 45,000 miles. Report the p-value. (10 points)
4. Hypothesis testing: Consumer Reports wanted to test a claim that Apple had on a tablet computer that it will last five years. They tested 25 tablets that had an average life of 5.25 years with a s = .7 years. Test at alpha .05 to see if average life differs from five years. (10 points)
5. Hypothesis testing for Proportions (10 points): North Beach Plantation in North Myrtle Beach, South Carolina has over 15,000 guests stay annually each year. Management has recently made many upgrades at their resort including facility updates (rooms, pools, dining), new family activities, and total quality management training for staff members (housing keeping, front desk, etc.). Management is striving for greater than 80° o of guests to be "very satisfied" with their stay. After the first few weeks, 200 guests were interviewed, 166 guests said they were "very satisfied". Test at alpha =--.05 to see if satisfaction is greater than 80%.
6. P-values (4 points) lithe alpha level for a large one tailed hypothesis test on the mean is .05, comment on your decision on the null hypothesis if the p value is:
a. p-value .03 decision:
b. p-value - .08 decision:
7. Hypothesis testing (10 points): It was estimated that UE business graduates will start at a higher salary than their cross-town rival school. A sample of 36 2012 recent business graduates from UE go ) had: a sample mean of $49,000, s $3,000, and 49 2012 business graduates from the rival school (4% ) had: a sample mean of $38,500, s $4,000, Test at alpha .10 to see if UE students are starting at a higher salary than their rival school in the market after graduation.
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