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MG 620 Research and statistics for Managers

Final Exam Instructions: Answer all questions


Part I : Problem

  • Fitting a straight line to a set of data yields the following prediction line:

Y = 4 + 3X

Interpret the meaning of the Y intercept, b0.

b0 is the value of Y when X is 0

ii) Interpret the meaning of the slope, b1

b1 mean that a unit change in X will increase Y by 3 units.

iii) Predict the mean value of Y for X = 5

+3X

  • +5(5)

  • What is the difference between the standard deviation, standard error of the mean, and standard error of the estimate? Discuss

The standard deviation measures the amount of variability or dispersion for a subject set of data from the mean, while the standard error of the mean measures how far the sample mean of the date is likely to be from the true population mean. The standard error is an estimate of the standard deviation of a statistic. , it is used to compute the confidence intervals and margins of error.

  • In a sample of size of 5, the sum of all values is 200. What is the sample mean

20 c. 800

40 d. None of the above

SHOW YOUR WORK!

Mean /n∑Xi

/5(200)

The following are the durations in minutes of a sample of long-distance phone calls within the continental United States reported by one long-distance carrier

Table 1

Time (in minutes) Relative Frequency

0 but less than 5 0.37

5 but less than 10 0.22

10 but less than 15 0.15

15 but less than 20 0.10

20 but less than 25 0.07

25 but less than 30 0.07

30 or more 0.02

  • Referring to Table 1, what is the width of each class?

1 minute c. 5 minutes

2% d. 100%

SHOW YOUR WORK!

  • Width refers to the difference between the lower limit of any two consecutive classes
  • 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 including which variable is independent and dependent.

Y

X

b) Estimate the intercept (b0). Show your work

X

Y

X⋅Y

X⋅X

1

4

4

1

2

6

12

4

1

3

3

1

0

1

0

0

1

1

1

1

∑X , ∑Y , ∑X⋅Y , ∑X

.5 is the value of Y when

c) Estimate the slope (b1). Show your work

c) Draw the regression line

d) Is the relationship positive or negative? Explain

Positive as Y increases with increase in X (Regression line is upward sloping)

  • If SSR = 76 and SST = 98, and n = 12
    • Determine the coefficient of determination, r2, and interpret its meaning.

r = SSR/SST

r /.7755

  • Compute the standard error of the estimate.
  • Draw the normal curve and indicate the mean, standard deviation, and the X bar scale

  • Identify the area of interest (that is shade the area under the curve that you will compute the probability).
  • Covert the X bar values in Z scores
  • P(X<4)(Z<)
  • Look up the Z standardized table for the cumulative area(s).
  • Now, make your decision ( that a customer will wait for less than 4 minutes)
    • Draw the normal curve and indicate the mean, standard deviation, and the X bar scale
    • Identify the area of interest (that is shade the area under the curve that you will compute the probability).
    • Covert the X bar values in Z scores
    • Look up the Z standardized table for the cumulative area(s).
    • Now, make your decision ( that a customer will have to wait for 4 to 8 minutes)

0.4772>0.05 Therefore customer will have to wait for 4 to 8 minutes is significant with probability of 0.4772

Five hundred employees were selected from a city’s large private companies, and they were asked whether or not they have any retirement benefits provided by their companies. Based on this information, the following two-way contingency table was prepared.

Have Retirement Benefits

Yes No Total


Men 225 75

Women 150 50


Total

If one employee is selected at random from these 500 employees,

Find the probability that this employee is a woman

(200/(200+300).4

Has retirement benefits

(125+150)/(500).55

Has retirement benefits given the employee is a man

225/.45

Is a woman given that she does not have retirement benefits

  • 50/(50+75).4

  1. Use the given data to construct a frequency distribution. Lori asked 24 students how many hours they had spent doing homework during the previous week. The results are shown below:

Number of students Hours of study

1

11

2

10

3

11

4

9

5

11

6

11

7

15

8

12

9

11

10

8

11

13

12

10

13

10

14

13

15

11

16

10

17

13

28

11

19

10

20

12

21

10

22

13

23

12

24

9

Construct a frequency distribution, using 4 classes and a class width of 2 hours, and a lower limit of 8 for class 1.

Class (hour)

Frequency (No. of students)

8-12

19

12-14

4

14-16

1

16-18

0

  • An entrepreneur is considering the purchase of a coin-operated laundry. The current owner claims that over the past 10 years, the average daily revenue was $675 with a standard deviation of $75. A sample of 30 days reveals daily revenue of $625.

Consider H0: µ = 675 versus Ha: µ < 675

  • At the .05 level of significance , is there evidence that the average daily revenue is less than 675
    • Compute the p-value and interpret its meaning
    • Construct a 95% confidence interval estimate of the population mean revenue of coin-operated laundry.
  • 625±1.96*75/
  • 625±18.98
  • (606.02, 643.98)
    • Compare the results of (a) , (b), and (c). What conclusions do you reach?
  • State the Hypothesis
  • Make your decision with respect to each part of the question.

P(Z<-3.65)= 0.0001 this is the probability that mean is less than 675 Draw the normal distribution and identify the acceptance and rejection regions

H0: µ = 675 versus Ha: µ < 675


µ


There is no enough evidence that the average daily revenue is less than 675

MG 620 Research and statistics for Managers 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 = 4 + 3X i) Interpret the meaning of the Y intercept, b 0 . b 0 =4 is the value of Y when X is 0 ii) Interpret the meaning of the slope, b 1 b 1 =3 mean that a unit change in X will increase Y by 3 units. iii) Predict the mean value of Y for X = 5 Y=4+3X Y=4+5(5)=9 2. What is the difference between the standard deviation, standard error of the mean, and standard error of the estimate? Discuss The standard deviation measures the amount of variability or dispersion for a subject set of data from the mean, while the standard error of the mean measures how far the sample mean of the date is likely to be from the true population mean. The standard error is an estimate of the standard deviation of a statistic. , it is used to compute the confidence intervals and margins of error. Dr. D Rawana Final Winter 2016 Page 1
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3. In a sample of size of 5, the sum of all values is 200. What is the sample mean a. 20 c. 800 b. 40 d. None of the above SHOW YOUR WORK! Mean =1/n∑Xi Mean=1/5(200)=40 The following are the durations in minutes of a sample of long-distance phone calls within the continental United States reported by one long-distance carrier Table 1 Time (in minutes) Relative Frequency 0 but less than 5 0.37 5 but less than 10 0.22 10 but less than 15 0.15 15 but less than 20 0.10 20 but less than 25 0.07 25 but less than 30 0.07 30 or more 0.02 4. Referring to Table 1, what is the width of each class? a. 1 minute c. 5 minutes b. 2% d. 100% SHOW YOUR WORK! Dr. D Rawana Final Winter 2016 Page 2
Background image of page 02
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