1. A manufacturer produces light bulbs that have a mean life of 500 hours when the production process is working properly. Based on experience, the population standard deviation is 50 hours and the light bulb life is normally distributed. The operations manager stops the production process if there is evidence that the population mean light bulb life is not equal to 500 hours.Please label each answer section with the corresponding letter.(1 point)

a. What are the appropriate H0 and H1 for hypothesis testing?

b. Using a level of significance =0.05, what are the rejection and non-rejection regions in the unit of hours if we use the sample mean of 100 randomly selected light bulbs as the test statistic?

c. A sample of 100 light bulbs was selected, and their mean is 485 hours. What is your conclusion on the hypotheses based on part a and part b?

d. What is the p-value associated with the sample mean equal to 485?

2. A real estate builder wishes to determine how house size (House, measured in square feet) is influenced by family income (Income, measured in dollars) and family size (Size, measured in number of people).The builder randomly selected 50 families and ran the multiple regression. Partial Microsoft Excel output is provided below.Please label each answer section with the corresponding letter.(1 point)

coefficient p-value

intercept -5.5146 0.0449

income 0.0413 0.0000

size 50.5423 0.0020

a. whatis the linear regression equation based on the excel output?

b. what is the predicted house size for an individual earning an annual income of $40,000 and having a family size of 4?

c. what annual income would an individual with a family size of 5 need to attain a predicted 5,000 square foot home?

3. A logistic regression model was built to predict the success to graduate froma MBA program for students who are currently applying based on their GMAT and GPA. Success is coded as 1 and failure 0. The google sheet logistic regression output is below, which predicts the probability of being 1. (1 point)

Coefficients Standard Error P-value Odd Ratio Lower 95% Upper 95%

Intercept -121.95 59.20119504 0.0394021951 0 0 0.002685230304

GPA 8.052816 5.019529214 0.0476485762 3142.632957 0.1677500457 58874153.26

GMAT 0.157291 0.07595908202 0.03838376102 1.1703361 1.008449404 1.358210518

a. What is the logistic regression equation based on the output where the left hand side of the equation is the predicted probability of success?

b. One of the admission criteria is the predicted probability of success needs to be higher than 60%. Among the following applicants, who will not be accepted based on this criterion alone?

Applicants GPA GMAT

a 3.64 573

b 3.36 594

c 3.66 594

d 3.11 599

e 3.10 608

f 3.24 616

g 2.93 617

h 3.37 619

c. For applicants who got admitted, 15% of them didn't complete the degree. And Graduates from this program in the past on average increased their salary by 10K every year for the first three years after graduation, (i.e., +10k year 1, +20k year 2, +30k year 3 relative to the salary before obtaining the degree).If we only consider the incremental earning potentials for the first three years and assume time value of money is negligible, what is the fair tuition for this program?