MGSC 309

Introduction to Business Statistics




 

Quiz May 6                                             Name: __________________

 

 

1.         A sample of 28 elements is selected to estimate a 95% confidence interval for the variance of the population.  The chi-square values to be used for this interval estimation are

            a.   -1.96 and 1.96

            b.   14.5733 and 43.1944

            c.   16.1513 and 40.1133

            d.   12.8786 and 46.9630

            Answer:  b

 

2.         The value of F.05 with 8 numerator and 19 denominator degrees of freedom is

            a.   2.48

            b.   2.58

            c.   3.63

            d.   2.96

            Answer:  a

 

3.         The symbol used for the variance of the population is

            a.   s

            b.   s2

            c.   S

            d.   S2

            Answer:  b

 

4.         The manager of the service department of a local car dealership has noted that the service times of a sample of 15 new automobiles has a standard deviation of 4 minutes.  A 95% confidence interval estimate for the standard deviation of the population is

            a.   2 to 4

            b.   2 to 3.95

            c.   2.93 to 6.31

            d.   8.58 to 39.79

            Answer:  c

 

5.         The number of degrees of freedom for the appropriate chi-square distribution in a test of independence is

            a.   n-1

            b.   K-1

            c.   number of rows minus 1 times number of columns minus 1

            d.   a chi-square distribution is not used

            Answer:  c

 

6.         The degrees of freedom for a contingency table with 12 rows and 12 columns is

            a.   144

            b.   121

            c.   12

            d.   120

            Answer:  b

 

Exhibit 1-1: The table below gives beverage preferences for random samples of teens and adults.

 

                                               Teens            Adults               Total

                        Coffee                50                  200                  250

                        Tea                  100                  150                  250

                        Soft Drink        200                  200                  400

                        Other                 50                    50                   100

                                                400                  600                 1,000

 

We are asked to test for independence between age (i.e., adult and teen) and drink preferences.

 

7.         Refer to Exhibit 1-1.  With a .05 level of significance, the critical value for the test is

            a.   1.645

            b.   7.815

            c.   14.067

            d.   15.507

            Answer:  b

 

8.         Refer to Exhibit 1-1.  The expected number of adults who prefer coffee is

            a.   0.25

            b.   0.33

            c.   150

            d.   200

            Answer:  c

 

9.         Refer to Exhibit 1-1.  The calculated value for this test for independence is

            a.   0

            b.   8.4

            c.   62.5

            d.   82.5

            Answer:  c

 

10.       Refer to Exhibit 1-1.  The result of the test is that the

            a.   hypothesis of independence can be rejected

            b.   hypothesis of independence cannot be rejected

            c.   test is inconclusive

            d.   None of these alternatives is correct.

            Answer:  a

 

11.       In an analysis of variance problem if SST = 120 and SSR = 80, then SSE is

            a.   200

            b.   40

            c.   80

            d.   120

            Answer:  b

 

12.       The mean square is the sum of squares divided by

            a.   the total number of observations

            b.   its corresponding degrees of freedom

            c.   its corresponding degrees of freedom minus one

            d.   None of these alternatives is correct.

            Answer:  b

 

13.       The critical F value with 8 numerator and 29 denominator degrees of freedom at

            a = 0.01 is

            a.   2.28

            b.   3.20

            c.   3.33

            d.   3.64

            Answer:  b

 

Ten observations were selected from each of 3 populations, and an analysis of variance was performed on the data.  The following are the results:

 

            Source of            Sum of               Degrees of               Mean

            Variation             Squares               Freedom                Square                 F  

            Between

            Groups                    82.4

 

            Within

            Groups                   158.4

           

                                                                                                                                

 

14.       Fill in the blanks in the above ANOVA table

 

 

15.       Using a = .05, test to see if there is a significant difference among the means of the three populations.

           

 

            Answers:

            a.   Ho:  m1 = m2 = m3

                  Ha:  at least one mean is different

                  F = 7.02 > 3.35; reject Ho

 

16.       A regression analysis between sales (Y in $1000) and advertising (X in dollars) resulted in the following equation

 

             = 30,000 + 4 X

 

            The above equation implies that an

            a.   increase of $4 in advertising is associated with an increase of $4,000 in sales

            b.   increase of $1 in advertising is associated with an increase of $4 in sales

            c.   increase of $1 in advertising is associated with an increase of $34,000 in sales

            d.   increase of $1 in advertising is associated with an increase of $4,000 in sales

            Answer:  d

 

17.       In a regression and correlation analysis if r2 = 1, then

            a.   SSE must also be equal to one

            b.   SSE must be equal to zero

            c.   SSE can be any positive value

            d.   SSE must be negative

            Answer:  b

 

18.       In a regression analysis if SSE = 200 and SSR = 300, then the coefficient of determination (R squared) is

            a.   0.6667

            b.   0.6000

            c.   0.4000

            d.   1.5000

            Answer:  b

 

19.       Regression analysis was applied between demand for a product (Y) and the price of the product (X), and the following estimated regression equation was obtained.

 

             = 120 - 10 X

 

            Based on the above estimated regression equation, if price is increased by 2 units, then demand is expected to

            a.   increase by 120 units

            b.   increase by 100 units

            c.   increase by 20 units

            d.   decease by 20 units

            Answer:  d

 

20.       If the coefficient of correlation is 0.8, the percentage of variation in the dependent variable explained by the variation in the independent variable is

            a.   0.80%

            b.   80%

            c.   0.64%

            d.   64%

            Answer:  d

 

21.       Regression analysis was applied between sales (in $10,000) and advertising (in $100) and the following regression function was obtained.

 

             = 50 + 8 X

 

            Based on the above estimated regression line if advertising is $1,000, then the point estimate for sales (in dollars) is

            a.   $8,050

            b.   $130

            c.   $130,000

            d.   $1,300,000

            Answer:  d

 

Exhibit 14-2

You are given the following information about y and x.

 

                                    y                                        x

                       Dependent Variable       Independent Variable

                                   5                                           1

                                   4                                           2

                                   3                                           3

                                   2                                           4

                                   1                                           5

 

22.       Refer to Exhibit 14-2.  The least squares estimate of b1 equals

            a.   1

            b.   -1

            c.   6

            d.   5

            Answer:  b

 

23.       Refer to Exhibit 14-2.  The least squares estimate of b0 equals

            a.   1

            b.   -1

            c.   6

            d.   5

            Answer:  c

 

 

Shown below is a portion of an Excel output for regression analysis relating Y (dependent variable) and X (independent variable).

 

ANOVA

 

 

 

 

 

 

df

SS

MS

F

Significance F

Regression

1

110

 

 

 

Residual

8

74

 

 

 

Total

9

184

 

 

 

 

 

 

 

 

 

 

Coefficients

Standard Error

T stat

P

 

Intercept

39.2222

5.9425

 

 

 

x

-0.5556

0.1611

 

 

 

 

24.       What has been the sample size for the above?

 

 

 

25.       Perform a t-test and determine whether or not X and Y are related.  Let a = 0.05.

 

 

26.       Perform an F-test and determine whether or not X and Y are related.  Let a = 0.05.

 

 

 

27.       Compute the coefficient of determination.

 

 

 

28.       Interpret the meaning of the value of the coefficient of determination that you found in d.  Be very specific.

 

 

 

 

29.       Fill in the blanks in the above

 

 

            Answers:  a through e

ANOVA

 

 

 

 

 

 

df

SS

MS

F

Significance F

Regression

1

110

110

11.8919

0.0087

Residual

8

74

9.25

 

 

Total

9

184

 

 

 

 

 

 

 

 

 

 

Coefficients

Standard Error

t Stat

P-value

 

Intercept

39.2222

5.9425

6.6003

0.0002

 

x

-0.5556

0.1611

-3.4485

0.0087

 

 

 

30.       In simple linear regression analysis, which of the following is not true?

            a.   The F test and the t test yield the same results.

            b.   The F test and the t test may or may not yield the same results.

            c.   The relationship between X and Y is represented by means of a straight line.

            d.   The value of F = t2.

            Answer:  b

 

 

 

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