MG 620 Research and statistics for Managers April 2016 Final Exam

MG 620 Research and statistics for Managers April 2016

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

1. Construct a scatter diagram for these data. Does the scatter diagram show a linear relationship between sales and number of new clients? Explain and show all work!

Y

6

5

4

3

2

1

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!

Instructions:

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 Z_STAT with the Z Tabled value.

5.      Make you decision