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Homework answers / question archive / Qatar University MAGT 304 ch14 1)In one-way ANOVA, the amount of total variation that is unexplained is measured by the: a

Qatar University MAGT 304 ch14 1)In one-way ANOVA, the amount of total variation that is unexplained is measured by the: a

Management

Qatar University

MAGT 304

ch14

1)In one-way ANOVA, the amount of total variation that is unexplained is measured by the:

a.

sum of squares for treatments.

b.

sum of squares for error.

c.

total sum of squares.

d.

degrees of freedom.

 

 

 

 

 

     2.   The test statistic of the single-factor ANOVA equals:

a.

sum of squares for treatments / sum of squares for error.

b.

sum of squares for error / sum of squares for treatments.

c.

mean square for treatments / mean square for error.

d.

mean square for error / mean square for treatments.

 

 

 

 

     3.   In a single-factor analysis of variance, MST is the mean square for treatments and MSE is the mean square for error. The null hypothesis of equal population means is rejected if:

a.

MST is much smaller than MSE.

b.

MST is much larger than MSE.

c.

MST is equal to MSE.

d.

None of these choices.

 

 

 

 

     4.   Which of the following is not a required condition for one-way ANOVA?

a.

The sample sizes must be equal.

b.

The populations must all be normally distributed.

c.

The population variances must be equal.

d.

The samples for each treatment must be selected randomly and independently.

 

 

 

 

     5.   The analysis of variance is a procedure that allows statisticians to compare two or more population:

a.

means.

b.

proportions.

c.

variances.

d.

standard deviations.

 

 

 

 

     6.   The distribution of the test statistic for analysis of variance is the:

a.

normal distribution.

b.

Student t-distribution.

c.

F-distribution.

d.

None of these choices.

 

 

 

     7.   In a one-way ANOVA, error variability is computed as the sum of the squared errors, SSE, for all values of the response variable. This variability is the:

a.

the total variation.

b.

within-treatments variation.

c.

between-treatments variation.

d.

None of these choices.

 

 

 

 

     8.   In the one-way ANOVA where there are k treatments and n observations, the degrees of freedom for the F-statistic are equal to, respectively:

a.

n and k.

b.

k and n.

c.

nk and k1.

d.

k1 and nk.

 

 

 

 

     9.   In the one-way ANOVA where k is the number of treatments and n is the number of observations in all samples, the degrees of freedom for treatments is given by:

a.

k1

b.

nk

c.

n1

d.

nk + 1

 

 

 

 

   10.   In ANOVA, the F-test is the ratio of two sample variances. In the one-way ANOVA (completely randomized design), the variance used as a numerator of the ratio is:

a.

mean square for treatments.

b.

mean square for error.

c.

total sum of squares.

d.

None of these choices.

 

 

 

 

   11.   In a completely randomized design for ANOVA, the numerator and denominator degrees of freedom are 4 and 25, respectively. The total number of observations must equal:

a.

24

b.

25

c.

29

d.

30

 

 

 

 

   12.   The number of degrees of freedom for the denominator in one-way ANOVA test involving 4 population means with 15 observations sampled from each population is:

a.

60

b.

19

c.

56

d.

45

 

 

 

   13.   The value of the test statistic in a completely randomized design for ANOVA is F = 6.29. The degrees of freedom for the numerator and denominator are 5 and 10, respectively. Using an F table, the most accurate statements to be made about the p-value is that it is:

a.

greater than 0.05

b.

between 0.025 and 0.050.

c.

between 0.010 and 0.025.

d.

between 0.001 and 0.010.

 

 

 

 

   14.   In one-way ANOVA, the term

 refers to the:

 

a.

sum of the sample means.

b.

sum of the sample means divided by the total number of observations.

c.

sum of the population means.

d.

weighted average of the sample means.

 

 

 

 

   15.   For which of the following is not a required condition for ANOVA?

a.

The populations are normally distributed.

b.

The population variances are equal.

c.

The samples are independent.

d.

All of these choices are required conditions for ANOVA.

 

 

 

 

   16.   One-way ANOVA is applied to independent samples taken from three normally distributed populations with equal variances. Which of the following is the null hypothesis for this procedure?

a.

1 + 2 + 3 = 0

b.

1 + 2 + 3  0

c.

1 = 2 = 3 = 0

d.

1 = 2 = 3

 

 

 

 

   17.   In the one-way ANOVA where k is the number of treatments and n is the number of observations in all samples, the number of degrees of freedom for error is:

a.

k1

b.

nk

c.

n1

d.

nk + 1

 

 

 

 

   18.   How does conducting multiple t-tests compare to conducting a single F-test?

a.

Multiple t-tests increases the chance of a Type I error.

b.

Multiple t-tests decreases the chance of a Type I error.

c.

Multiple t-tests does not affect the chance of a Type I error.

d.

This comparison cannot be made without knowing the number of populations.

 

 

 

 

       

 

  19.  In one-way analysis of variance, between-treatments variation is measured by the:

a.

SSE

b.

SST

c.

SS(Total)

d.

standard deviation

 

 

 

   20.   One-way ANOVA is applied to independent samples taken from four normally distributed populations with equal variances. If the null hypothesis is rejected, then we can infer that

a.

all population means are equal.

b.

all population means differ.

c.

at least two population means are equal.

d.

at least two population means differ.

 

 

 

   21.   Consider the following partial ANOVA table:

 

Source of Variation

SS

df

MS

F

Treatments

  75

*

25      

6.67

Error

  60

*

3.75

 

Total

135

19

 

 

 

The numerator and denominator degrees of freedom for the F-test (identified by asterisks) are

a.

4 and 15

b.

3 and 16

c.

15 and 4

d.

16 and 3

 

 

 

   22.   Consider the following ANOVA table:

 

Source of Variation

SS

df

MS

F

Treatments

  4

  2

2.0

0.80

Error

30

12

2.5

 

Total

34

14

 

 

 

The number of treatments is

a.

13

b.

5

c.

3

d.

12

 

 

 

   23.   In one-way analysis of variance, within-treatments variation is measured by:

a.

sum of squares for error.

b.

sum of squares for treatments.

c.

total sum of squares.

d.

standard deviation.

 

 

   24.   Consider the following ANOVA table:

 

Source of Variation

SS

df

MS

F

Treatments

128

  4

32  

2.963

Error

270

25

10.8

 

Total

398

29

 

 

 

The total number of observations is:

a.

25

b.

29

c.

30

d.

32

 

 

 

   25.   In one-way analysis of variance, if all the sample means are equal, then the:

a.

total sum of squares is zero.

b.

sum of squares for error is zero.

c.

sum of squares for treatments is zero.

d.

sum of squares for error equals sum of squares for treatments.

 

 

 

   26.   Which of the following components in an ANOVA table is not additive?

a.

Sum of squares

b.

Degrees of freedom

c.

Mean squares

d.

All of these choices are additive.

 

 

 

   27.   In which case can an F-test be used to compare two population means?

a.

For one tail tests only.

b.

For two tail tests only.

c.

For either one or two tail tests.

d.

None of these choices.

 

 

 

   28.   The F-test statistic in a one-way ANOVA is equal to:

a.

MST/MSE

b.

SST/SSE

c.

MSE/MST

d.

SSE/SST

 

 

 

   29.   The numerator and denominator degrees of freedom for the F-test in a one-way ANOVA are, respectively,

a.

(nk) and (k1)

b.

(k1) and (nk)

c.

(kn) and (n1)

d.

(n1) and (kn)

 

 

 

          

   30.   Which of the following statements is false?

a.

F = t2

b.

The F-test can be used instead of a two tail t-test when you compare two population means.

c.

Doing three t-tests is statistically equivalent to doing one F-test when you compare three population means.

d.

All of these choices are true.

 

 

 

 

   31.   Which of the following statements about multiple comparison methods is false?

a.

They are to be use once the F-test in ANOVA has been rejected.

b.

They are used to determine which particular population means differ.

c.

There are many different multiple comparison methods but all yield the same conclusions.

d.

All of these choices are true.

 

 

 

 

32. When the objective is to compare more than two populations, the experimental design that is the counterpart of the matched pairs experiment is called a:

a.

completely randomized design.

b.

one-way ANOVA design.

c.

randomized block design.

d.

None of these choices.

 

 

 

 

   33.   In the randomized block design for ANOVA, where k is the number of treatments and b is the number of blocks, the number of degrees of freedom for error is:

a.

kb

b.

nkb + 1

c.

kb1

d.

None of these choices.

 

 

 

 

   34.   Which of the following is false regarding SSB?

a.

SSB stands for sum of squares for blocks.

b.

SSB can help to reduce SSE.

c.

SSB can help make it easier to determine whether differences exist between the treatment means.

d.

All of these choices are true.

 

 

 

 

   35.   The primary interest of designing a randomized block experiment is to:

a.

reduce the variation among blocks.

b.

increase the between-treatments variation to more easily detect differences among the treatment means.

c.

reduce the within-treatments variation to more easily detect differences among the treatment means.

d.

None of these choices.

 

 

 

 

   36.   The randomized block design with exactly two treatments is equivalent to a two-tail:

a.

independent samples z-test.

b.

independent samples equal-variances t-test.

c.

independent samples unequal-variances t-test.

d.

matched pairs t-test.

 

 

 

 

   37.   In the randomized block design ANOVA, the sum of squares for error equals:

a.

SS(Total)SST

b.

SS(Total)SSB

c.

SS(Total)SSTSSB

d.

None of these choices.

 

 

 

 

   38.   A randomized block design with 4 treatments and 5 blocks produced the following sum of squares values: SS(Total) = 1,951, SST = 349, SSE = 188 . The value of SSB must be:

a.

1,414

b.

537

c.

1,763

d.

1,602

 

 

 

 

       

 

 

 

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