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MULTIPLE CHOICE. 1) A national car...

MULTIPLE CHOICE.

1) A national car rental company recently conducted a study recently in which cars with automatic

and standard transmissions (factor A-Sample) were rented to male and female customers (factor B

-Columns). Three customers in each category were randomly selected and the miles driven per

day was recorded as follows:

Males Females

Automatic 124 54

55 88

78 76

Standard 33 88

108 90

156 115

Based on these sample data, and alpha = .05, which of the following statements is true?

A) The means for factor A are significantly different.

B) The means for factor B are significantly different.

C) There is no significant interaction between factors A and B.

D) All of the above statements are true.

2) An Internet service provider is interested in testing to see if there is a difference in the mean weekly

connect time for users who come into the service through a dial-up line, DSL, or cable Internet. To

test this, the ISP has selected random samples from each category of user and recorded the connect

time during a week period. The following data were collected:

Dial Up DSL Cable

19.2 40.6 39.5

17.7 40 42.3

17.2 41.5 47

18.9 30.5 45.4

26.9 46.8 41.1

22.6 43.2

31.2 39.9

41.9

49.3

Assuming that the test is to be conducted at a 0.01 level of significance, what would the critical

value be for this test?

A) F = 6.013 B) F = 1.93 C) F = 3.555 D) t = 2.8784

3) Which type of ANOVA can include interaction? 3)

A) One-way B) All types of ANOVA

C) Randomized complete block D) Two-factor

4) Which of the following is the minimum number of required replications per cell for a two-factor

ANOVA design if you plan to test for interactive effects between factors A and B?

A) 2 B) 5 C) 1 D) 3

5) A major consumer group recently undertook a study to determine whether automobile customers

would rate the quality of cars differently that were manufactured in the U.S., Europe, or Japan. To

conduct this test, a sample of 20 individuals was asked to look at mid-range model cars made in

each of the three countries. The individuals in the sample were then asked to provide a rating for

each car on a scale of 1 to 1000. The following computer output resulted, and the tests were

conducted using a significance level equal to 0.05.

Anova: Two-Factor Without Replication

SUMMARY Count Sum Average Variance

1 3 2473.08 824.36 740.996

2 3 2411.911 8 0 3. 9 705 1120 . 791

3 3 2495.924 831 . 9748 2958. 509

4 3 2494.92 831.64 489.802

5 3 2487.995 829. 3318 1129. 897

6 3 2351.078 783. 6925 443. 6333

7 3 2319.392 773. 1308 4450. 131

8 3 2373.183 791. 0609 468. 4032

9 3 2350. 24 783 . 4132 2173 . 944

10 3 2416.553 805. 5178 1200. 471

11 3 2479.895 826. 6317 905. 5771

12 3 2393.605 797. 8684 382. 9982

13 3 2245.545 748.515 11513.88

14 3 2361.247 787. 0824 1364. 083

15 3 2418.24 806.08 1147. 566

16 3 2379.708 793. 2361 3115. 073

17 3 2494.709 831. 5696 3092. 78

18 3 2389.693 796. 5643 5503. 197

19 3 2358.984 786. 3279 6874. 581

20 3 2273.107 757. 7023 15. 62739

US 20 15708.57 785. 4287 1867. 925

Germany 20 16453.12 822. 6558 1841. 004

Japan 20 15807.32 790. 366 2408. 399

ANOVA

Source of Variation SS df MS F P-value F crit

Rows 34378.73 19 1809.407 0.840232 0.649989 1.867331

Columns 16352.4 2 8176.198 3.796773 0.031385 3.244821

Error 81831.48 38 2153.46

Total 132562.6 59

Based upon the data, which of the following statements is true?

A) The averages for the 20 people are not all the same.

B) Blocking was effective.

C) The primary null hypothesis should not be rejected.

D) Blocking was not effective.

6) Many companies use well-known celebrities as spokespeople in their TV advertisements. A study

was conducted to determine whether brand awareness of female TV viewers and the gender of the

spokesperson are independent. Each in a sample of 300 female TV viewers was asked to identify a

product advertised by a celebrity spokesperson. The gender of the spokesperson and whether or

not the viewer could identify the product was recorded. The numbers in each category are given

below.

Male Celebrity Female Celebrity

Identified product 41 61

Cound not identify 109 89

Referring to these sample data, if the appropriate hypothesis test is to be conducted using a .05 level

of significance, which of the following is correct critical value?

A) 9.4877 B) 1.96 C) 3.8415 D) 7.8147

7) A walk-in medical clinic believes that arrivals are uniformly distributed over weekdays (Monday

through Friday). It has collected the following data based on a random sample of 100 days.

Frequency

Mon 25

Tue 22

Wed 19

Thu 18

Fri 16

Total 100

Based on these data, conduct a goodness-of-fit test using a 0.10 level of significance. Which

conclusion is correct?

A) Arrivals are uniformly distributed over the weekday because (test statistic) > (critical value).

B) Arrives are uniformly distributed over the weekday because (test statistic) < (critical value).

C) Arrivals are not uniformly distributed over the weekday because (test statistic) < (critical

value).

D) Arrivals are not uniformly distributed over the weekday because (test statistic) > (critical

value).

8) The State Transportation Department is thinking of changing its speed limit signs. It is considering

two new options in addition to the existing sign design. At question is whether the three sign

designs will produce the same mean speed. To test this, the department has conducted a limited

test in which a stretch of roadway was selected. With the original signs up, a random sample of 30

cars was selected and the speeds were measured. Then, on different days, the two new designs

were installed, 30 cars each day were sampled, and their speeds were recorded. Suppose that the

following summary statistics were computed based on the data:

xbar1 = 62.1 xbar2 = 58.94 xbar3 = 71.2

Based on these sample results and significance level equal to 0.05, what is the critical value for this

hypothesis test?

A) F = approximately 29.47 B) F = approximately 2.70

C) F = approximately 3.15 D) F = approximately 4.90

9) A walk-in medical clinic believes that arrivals are uniformly distributed over weekdays (Monday through Friday). It has collected the following data based on a random sample of 100 days.

Frequency

Mon 25

Tue 22

Wed 19

Thu 18

Fri 16

Total 100

Assuming that a goodness-of-fit test is to be conducted using a 0.10 level of significance, the

critical value is:

A) 11.0705. B) 9.4877. C) 9.2363. D) 7.7794.

10) A large orchard owner in the state of Washington is interested in determining whether the mean

number of bushels of peaches per acre is the same or different depending on the type of tree that is

used. He also thinks that production may be affected by the type of fertilizer that is used. To test, he

has set up a test in which a one-acre plot of peach trees with a combination each of 5 varieties and 3

fertilizer types are studied. In this case, the number of treatments is:

A) 3.

B) 5.

C) 15.

D) Can't be determined without knowing how many trees are planted on each acre.

TRUE/FALSE.

11) Prior to performing a one-way analysis of variance test, the analysts were interested in

determining whether the population variances were equal. The design had one factor with 3 levels

and a balanced design with sample size equal to 6. Among others, the following summary statistics

were computed:

s2over1=50, s2over2=80, s2over3=40

Based on these statistics, the calculated F-value for performing a Hartley's F-test for equality of population variances is F = 2.00.

12) A randomized complete block analysis of variance allows the analyst to control for sources of

variation that might adversely affect the analysis by using the concept of paired samples.

13) In a contingency analysis the expected values are based on the assumption that the two variables

are independent of each other.

14) In a two-factor ANOVA design with replication, if the null hypothesis pertaining to interaction

between factors A and B is rejected, then it is recommended that the hypothesis tests for factor A

and factor B individually should not be conducted because the conclusions might be misleading.

15) If the test statistic for a chi-square goodness-of-fit test is larger than the critical value, the null

hypothesis should be rejected.

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