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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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