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[answered] ASSIGNMENT 4-7 WITH ANSWERS ASSIGNMENT 4 1. The sampling di


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ASSIGNMENT 4-7 WITH ANSWERS

 

ASSIGNMENT 4

 

1.

 

a.

 

b.

 

c.

 

d. The sampling distribution for a goodness of fit test is

 

the Poisson distribution

 

the t distribution

 

the normal distribution

 

the chi-square distribution 2.

 

a.

 

b.

 

c.

 

d. A goodness of fit test is always conducted as a

 

lower-tail test

 

upper-tail test

 

middle test

 

None of these alternatives is correct. 3.

 

a.

 

b.

 

c.

 

d. In order not to violate the requirements necessary to use the chi-square distribution, each

 

expected frequency in a goodness of fit test must be

 

at least 5

 

at least 10

 

no more than 5

 

less than 2 4.

 

a.

 

b.

 

c.

 

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

 

144

 

121

 

12

 

120 Exhibit 1

 

When individuals in a sample of 150 were asked whether or not they supported capital

 

punishment, the following information was obtained.

 

Do You Support

 

Number of

 

Capital Punishment

 

Individuals

 

Yes

 

40

 

No

 

60

 

No Opinion

 

50

 

We are interested in determining whether or not the opinions of the individuals (as to Yes, No, and No

 

Opinion) are uniformly distributed.

 

5.

 

a.

 

b.

 

c.

 

d. Refer to Exhibit 1. The expected frequency for each group is

 

0.333

 

0.50

 

1/3

 

50

 

1 ASSIGNMENT 4-7 WITH ANSWERS

 

6.

 

a.

 

b.

 

c.

 

d. Refer to Exhibit 1. The calculated value for the test statistic equals

 

2

 

-2

 

20

 

4 7.

 

a.

 

b.

 

c.

 

d. Refer to Exhibit 1. The conclusion of the test at 5% level of significance is that the?.

 

distribution is uniform

 

distribution is not uniform

 

test is inconclusive

 

None of these alternatives is correct. Exhibit 2

 

In order to determine whether or not a particular medication was effective in curing the common cold,

 

one group of patients was given the medication, while another group received sugar pills. The results of

 

the study are shown below.

 

Patients

 

Patients

 

Cured

 

Not Cured

 

Received medication

 

70

 

10

 

Received sugar pills

 

20

 

50

 

We are interested in determining whether or not the medication was effective in curing the common

 

cold.

 

8.

 

a.

 

b.

 

c.

 

d. Refer to Exhibit 2. The expected frequency of those who received medication and were cured is

 

70

 

150

 

28

 

48 9.

 

a.

 

b.

 

c.

 

d. Refer to Exhibit 2. The test statistic is

 

10.08

 

54.02

 

1.96

 

1.645 10. Refer to Exhibit 2. The hypothesis is to be tested at the 5% level of significance. The critical value

 

from the table equals

 

3.84

 

7.81

 

5.99

 

9.34 a.

 

b.

 

c.

 

d. 2 ASSIGNMENT 4-7 WITH ANSWERS

 

ASSIGNMENT 5

 

1.

 

a.

 

b.

 

c.

 

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

 

200

 

40

 

80

 

120 2. In an analysis of variance problem involving 3 treatments and 10 observations per treatment,

 

SSE = 399.6. The MSE for this situation is

 

133.2

 

13.32

 

14.8

 

30.0 a.

 

b.

 

c.

 

d.

 

3.

 

a.

 

b.

 

c.

 

d.

 

e. When an analysis of variance is performed on samples drawn from k populations, the mean

 

square between treatments (MSTR) is

 

SSTR/ nT

 

SSTR/ (nT - 1)

 

SSTR/k

 

SSTR/ (k - 1)

 

None of these alternatives is correct. 4.

 

a.

 

b.

 

c.

 

d. The critical F value with 6 numerator and 60 denominator degrees of freedom at ? = .05 is

 

3.74

 

2.25

 

2.37

 

1.96 5.

 

a.

 

b.

 

c.

 

d. The ANOVA procedure is a statistical approach for determining whether or not

 

the means of two samples are equal

 

the means of two or more samples are equal

 

the means of more than two samples are equal

 

the means of two or more populations are equal 6. An ANOVA procedure is applied to data obtained from 6 samples where each sample contains

 

20 observations. The degrees of freedom for the critical value of F are

 

6 numerator and 20 denominator degrees of freedom

 

5 numerator and 20 denominator degrees of freedom

 

5 numerator and 114 denominator degrees of freedom

 

6 numerator and 20 denominator degrees of freedom a.

 

b.

 

c.

 

d. 3 ASSIGNMENT 4-7 WITH ANSWERS

 

7.

 

a.

 

b.

 

c.

 

d. In the ANOVA, treatment refers to

 

experimental units

 

different levels of a factor

 

a factor

 

applying antibiotic to a wound 8.

 

a.

 

b.

 

c.

 

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

 

the total number of observations

 

its corresponding degrees of freedom

 

its corresponding degrees of freedom minus one

 

None of these alternatives is correct. 9. In factorial designs, the response produced when the treatments of one factor interact with the

 

treatments of another in influencing the response variable is known as

 

main effect

 

replication

 

interaction

 

None of these alternatives is correct. a.

 

b.

 

c.

 

d. Exhibit 1

 

SSTR = 6,750

 

SSE = 8,000

 

nT = 20 H0: ?1= ? 2= ? 3= ? 4

 

Ha: at least two means are different 10.

 

a.

 

b.

 

c.

 

d. Refer to Exhibit 1. The mean square between treatments (MSTR) equals

 

400

 

500

 

1,687.5

 

2,250 11.

 

a.

 

b.

 

c.

 

d. Refer to Exhibit 1. The mean square within treatments (MSE) equals

 

400

 

500

 

1,687.5

 

2,250 12.

 

a.

 

b.

 

c.

 

d. Refer to Exhibit 1. The test statistic to test the null hypothesis equals

 

0.22

 

0.84

 

4.22

 

4.5

 

4 ASSIGNMENT 4-7 WITH ANSWERS

 

13.

 

a.

 

b.

 

c.

 

d. Refer to Exhibit 1. The null hypothesis is to be tested at the 5% level of significance. The critical

 

value from the table is

 

2.87

 

3.24

 

4.08

 

8.7 14.

 

a.

 

b.

 

c.

 

d. Refer to Exhibit 1. The null hypothesis

 

should be rejected

 

should not be rejected

 

was designed incorrectly

 

None of these alternatives is correct. Exhibit 2

 

The following is part of an ANOVA table, which were the results of 3 treatments and a total of 15

 

observations. Source of Variation

 

Between Treatments

 

Within Treatments (Error)

 

Total Sum of

 

Squares

 

64

 

96 Degrees of

 

Freedom Mean

 

Square F 15.

 

a.

 

b.

 

c.

 

d. Refer to Exhibit 2. The number of degrees of freedom corresponding to between treatments is

 

12

 

2

 

3

 

4 16.

 

a.

 

b.

 

c.

 

d. Refer to Exhibit 2. The number of degrees of freedom corresponding to within treatments is

 

12

 

2

 

3

 

15 17.

 

a.

 

b.

 

c.

 

d. Refer to Exhibit 2. The mean square between treatments (MSTR) is

 

36

 

16

 

8

 

32 5 ASSIGNMENT 4-7 WITH ANSWERS

 

18.

 

a.

 

b.

 

c.

 

d.

 

19.

 

a.

 

b.

 

c.

 

d. Refer to Exhibit 2. If at a 5% level of significance, we want to determine whether or not the

 

means of the populations are equal, the critical value of F is

 

3.89

 

19.41

 

3.16

 

1.96

 

Refer to Exhibit 2. Based on the computed test statistic, the conclusion of the test is that the

 

means

 

are equal

 

may be equal

 

are not equal

 

None of these alternatives is correct. Exhibit 3 Source of Variation

 

Between Treatments

 

Between Blocks

 

Error

 

Total Sum of

 

Squares

 

2,073.6

 

6,000.0 Degrees of

 

Freedom

 

4

 

5

 

20

 

29 Mean

 

Square F 1,200

 

288 20.

 

a.

 

b.

 

c.

 

d. Refer to Exhibit 3. The null hypothesis for this ANOVA problem is

 

?1=?2=?3=?4

 

?1=?2=?3=?4=?5

 

?1=?2=?3=?4=?5=?6

 

?1=?2= ... =?20 21.

 

a.

 

b.

 

c.

 

d. Refer to Exhibit 3. The mean square between treatments equals

 

288

 

518.4

 

1,200

 

8,294.4 22.

 

a.

 

b.

 

c.

 

d. Refer to Exhibit 3. The sum of squares due to error equals

 

14.4

 

2,073.6

 

5,760

 

6,000 6 ASSIGNMENT 4-7 WITH ANSWERS

 

23.

 

a.

 

b.

 

c.

 

d. Refer to Exhibit 3. The test statistic to test the null hypothesis equals

 

0.432

 

1.8

 

4.17

 

28.8 24.

 

a.

 

b.

 

c.

 

d. Refer to Exhibit 3. The null hypothesis is to be tested at the 5% level of significance. The critical

 

value from the table is

 

2.71

 

2.87

 

5.19

 

5.8 25.

 

a.

 

b.

 

c.

 

d. Refer to Exhibit 3. The null hypothesis

 

should be rejected

 

should not be rejected

 

should be revised

 

None of these alternatives is correct. 1.

 

a.

 

b.

 

c.

 

d.

 

2.

 

a.

 

b.

 

c.

 

d.

 

3. ASSIGNMENT 6

 

The proportion of the variation in the dependent variable y that is explained by the estimated

 

regression equation is measured by the

 

correlation coefficient

 

standard error of the estimate

 

coefficient of determination

 

confidence interval estimate

 

In a residual plot against x that does not suggest we should challenge the assumptions of our

 

regression model, we would expect to see

 

a horizontal band of points centered near zero

 

a widening band of points

 

a band of points having a slope consistent with that of the regression equation

 

a parabolic band of points a.

 

b.

 

c.

 

d. The difference between the observed value of the dependent variable and the value predicted

 

by using the estimated regression equation is the

 

standard error

 

residual

 

prediction interval

 

variance 4.

 

a.

 

b.

 

c.

 

d. In regression analysis, the variable that is being predicted is the

 

dependent variable

 

independent variable

 

intervening variable

 

None of these answers is correct.

 

7 ASSIGNMENT 4-7 WITH ANSWERS

 

5.

 

a.

 

b.

 

c.

 

d. In regression analysis if the dependent variable is measured in dollars, the independent variable

 

must also be in dollars

 

must be in some unit of currency

 

can be any units

 

cannot be in dollars Exhibit 1: A regression analysis resulted in the following information regarding a dependent variable (y)

 

and an independent variable (x).

 

n = 10

 

?x = 55

 

?y = 55

 

?x2 = 385

 

?y2 = 385

 

?xy = 220

 

6.

 

a.

 

b.

 

c.

 

d. Refer to Exhibit 1. The least squares estimate of b1 equals

 

1

 

-1

 

5.5

 

11 7.

 

a.

 

b.

 

c.

 

d. Refer to Exhibit 1. The least squares estimate of b0 equals

 

1

 

-1

 

5.5

 

11 8.

 

a.

 

b.

 

c.

 

d. Refer to Exhibit 1. The point estimate of y when x = 20 is

 

0

 

31

 

9

 

-9 9.

 

a.

 

b.

 

c.

 

d. Refer to Exhibit 1. The sample correlation coefficient equals

 

0

 

-1

 

+1

 

-0.5 10.

 

a.

 

b.

 

c.

 

d. Refer to Exhibit 1. The coefficient of determination equals

 

0

 

-1

 

+1

 

-0.5

 

8 ASSIGNMENT 4-7 WITH ANSWERS

 

Exhibit 2: You are given the following information about y and x.

 

Y:

 

Dependent

 

Variable X:

 

Independent

 

Variable 5

 

7

 

9

 

11 15

 

12

 

10

 

7 11.

 

a.

 

b.

 

c.

 

d. Refer to Exhibit 2. The least squares estimate of b1 equals

 

-0.7647

 

-0.13

 

21.4

 

16.412 12.

 

a.

 

b.

 

c.

 

d. Refer to Exhibit 2. The least squares estimate of b0 equals

 

-7.647

 

-1.3

 

21.4

 

16.41176 13.

 

a.

 

b.

 

c.

 

d. Refer to Exhibit 2. The sample correlation coefficient equals

 

-86.667

 

-0.99705

 

0.9941

 

0.99705 14.

 

a.

 

b.

 

c.

 

d. Refer to Exhibit 2. The coefficient of determination equals

 

-0.99705

 

-0.9941

 

0.9941

 

0.99705 Exhibit 3: Regression analysis was applied between sales data (in $1,000s) and advertising data (in

 

$100s) and the following information was obtained.

 

= 12 + 1.8x

 

n = 17

 

SSR = 225

 

SSE = 75

 

sb1 = 0.2683

 

9 ASSIGNMENT 4-7 WITH ANSWERS 15.

 

a.

 

b.

 

c.

 

d. Refer to Exhibit 3. Based on the above estimated regression equation, if advertising is $3,000,

 

then the point estimate for sales (in dollars) is

 

$66,000

 

$5,412

 

$66

 

$17,400 16.

 

a.

 

b.

 

c.

 

d. Refer to Exhibit 3. The F statistic computed from the above data is

 

3

 

45

 

48

 

Not enough information is given to answer this question. 17.

 

a.

 

b.

 

c.

 

d. Refer to Exhibit 3. The critical F value at ? = 0.05 is

 

3.59

 

3.68

 

4.45

 

4.54 18.

 

a.

 

b.

 

c.

 

d. Refer to Exhibit 3. The t statistic for testing the significance of the slope is

 

1.80

 

1.96

 

6.709

 

0.555 19.

 

a.

 

b.

 

c.

 

d. Refer to Exhibit 3. Using ? = 0.05, the critical t value for testing the significance of the slope is

 

1.753

 

2.131

 

1.746

 

2.120 Exhibit 4: It has been found in research that as the age of miss America increases the number of

 

murders by steam, hot vapors and hot objects increases.

 

20.

 

a.

 

b. Refer to exhibit 4. Can we infer causation from what is explained in the problem?

 

Yes

 

No 21.

 

a.

 

b.

 

c.

 

d. Refer to exhibit 4. What type of correlation is observed in the problem?

 

Perfect correlation

 

Moderate negative correlation

 

Moderate positive correlation

 

Spurious correlation

 

10

 


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