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, b_{0}.

ii) Interpret the meaning of the slope, b_{1}

_{ }

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

- 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 **(b_{0}). Show your work

c) Estimate the **slope** (b_{1}). Show your work

c) **Draw the regression line**

3. If SSR = 75 and SST = 88, compute the coefficient of determination, **r ^{2}**, 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

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