MG 620 Research and statistics for Managers April 2016
Final Exam Instructions: Answer all questions
Part I : Problem
1. Fitting a straight line to a set of data yields the following prediction line:
Y = 10 + 4X
i) Interpret the meaning of the Y intercept, b0.
ii) Interpret the meaning of the slope, b1
iii) Predict the mean value of Y for X =8
2. College administrators are interested in determining if the number of hours students study affects the GPA of students. They sample 6 students and determine the number of hours of studied last month and their GPA. These data are presented in the table that follows.
Student Hours Study(X) GPA (Y)
1 1 4
2 2 6
3 1 3
4 0 1
5 1 1
6 2 5
0 1 2 3 X
b) Estimate the intercept (b0). Show your work
c) Estimate the slope (b1). Show your work
c) Draw the regression line
3. If SSR = 75 and SST = 88, compute the coefficient of determination, r2, and interpret its meaning.
4. A Professor at a Community College does not want its students to wait in line for service for too long. She estimated that the students currently have to wait an average of 4 minutes for service. Assume that the waiting times for all customers at this branch have a normal distribution with a mean of 8 minutes and a standard deviation of 2 minutes.
Find the probability that randomly selected customer will have to wait for less than 4 minutes?
Instructions: Show all steps:
1. Draw the normal curve and indicate the mean, standard deviation, and the X bar scale
2. Identify the area of interest (that is shade the area under the curve that you will compute the probability).
3. Covert the X bar values in Z scores
4. Look up the Z standardized table for the cumulative area(s).
5. Now, make your decision ( that a customer will wait for less than 4 minutes)
1. A Professor at a Community College does not want its students to wait in line for service for too long. She estimated that the students currently have to wait an average of 4 minutes for service. Assume that the waiting times for all customers at this branch have a normal distribution with a mean of 8 minutes and a standard deviation of 2 minutes.
What is the probability that customers have to wait for 2 to 8 minutes?
Instructions: Show all steps:
a. Draw the normal curve and indicate the mean, standard deviation, and the X bar scale
b. Identify the area of interest (that is shade the area under the curve that you will compute the probability).
c. Covert the X bar values in Z scores
d. Look up the Z standardized table for the cumulative area(s).
e. Now, make your decision ( that a customer will have to wait for 2 to 8 minutes)
10. One thousand teachers were selected from a city’s large private college, and they were asked whether or not they have health coverage provided by their college. Below is the two-way contingency table showing health care coverage.
Have Health Coverage
Yes No Total
Men 450 150 600
Women 300 100 400
Total 750 250 1000
Suppose a someone is selected at random from these 1000 teachers,
a) Find the probability that this person is a woman
b) What is the probability that a person selected is a woman and has health coverage
c) What is the probability that a teacher has health coverage given that the teacher is a man
d) What is the probability the teacher is a woman given that she does not have health coverage
11. A Motel owner wishes to sell his apartment. He claims that over the past 8 months, the average daily rent revenue was $200 with a standard deviation of $25. A sample of 30 days reveals daily revenue of $150.
If you use the significance level of α = .05, would you reject the null hypothesis? Show all steps!
1. State the Hypothesis( Null and Alternative)
2. Draw the normal distribution and identify the acceptance and rejection regions
3. Compute the Z STAT value
4. Compare your ZSTAT with the Z Tabled value.
5. Make you decision
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