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# STAT*2060DE F Assignment #6 | Complete Solution

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**STAT*2060DE F Questions for Assignment #6**

This will be another D2L quiz. Please input your responses before the deadline. Give at

least 3 decimal places where applicable.

Questions #1 - #8 refer to the following information.

Marketing organizations sometimes use a pupillometer, a device that used to observe

changes in pupil dilations as the eye is exposed to di erent visual stimuli, to help them

evaluate potential consumer interest in mew products, alternative package designs, and

other factors. Suppose one organization used a pupillometer to evaluate consumer reaction

to di erent silverware patterns for a client. 10 consumers were chosen at random, and each

was shown two silverware patterns. The pupillometer readings (in millimeters) are given

in the table below.

Consumer Pattern A Pattern B

1 1.12 1.21

2 0.97 1.04

3 0.87 1.05

4 0.97 1.11

5 1.01 1.08

6 1.01 1.15

7 0.88 1.02

8 1.41 1.07

9 1.18 1.20

10 1.08 1.14

N.B. We should NOT be using the independent samples method.

For the following questions, take the di erences using Pattern A Pattern B.

#1. What is the point estimate of the population mean di erence? [Hint: This value

should be negative]

#2. What is the standard error of the sample mean di erence?

#3. What is the 95% con dence interval for the population mean di erence?

A) (-.183, .069)

B) (-.173, .059)

C) (-.163, .049)

D) (-.153, .039)

E) (-.143, .029)

Carry out a test that the population mean di erence is equal to 0, against a two-sided

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alternative.

#4.What are the appropriate hypotheses?

A) H0 : = 0; Ha : > 0

B) H0 : = 0; Ha : 6= 0

C) H0 : 1 = 2; Ha : 1 > 2

D) H0 : p1 = p2; Ha : p1 6= p2

#5. What is the value of the appropriate test statistic? [Hint: This value should be

negative.]

#6. You cannot get an exact p-value from the t table, but you can get an appropriate

range of values. Which one of the following best represents what we can say about the

p-value based on the t table?

A) p-value <.001

B) .025 < p-value <.05

C) .05 < p-value <.10

D) .10 < p-value <.20

E) p-value >.20.

#7. Which one of the following is the most appropriate conclusion at = :05?

A) There is signi cant evidence the population mean di erence between the two patterns

is equal to 0.

B) There is signi cant evidence the population mean di erence between the two patterns

is not equal to 0.

C) There is not signi cant evidence that the population mean di erence di ers from 0.

D) All of the above.

#8. For the above test to be valid, we need the sample di erences to be a simple random

sample from population of di erences. What is the other assumption that we need? That

is, what else must be true in order for our methods to be reasonable?

A) The population mean di erence is known.

B) The population of di erences is normally distributed.

C) The two populations have equal variance.

D) The standard deviation of the population of di erences is known.

Questions 9-16 refer to the following information:

Suppose a hotel undergoes a renovation, with the notion of catering more toward male

clientele. One year after the renovations have been completed, the hotel conducts a survey

of 24 male and 18 female guests. One question on the survey asks the customers for an

overall satisfaction rating, between 0 and 100. The following table summarizes the results.

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Mean Rating Standard Deviation Sample size

Males 81.8 7.1 24

Females 62.1 6.8 18

It is impossible for the ratings to be perfectly normally distributed (one reason is they're

limited to the 0-100 range). The sample sizes are not very large, but they're not uncomfort-

ably small either. It's always useful to plot the data out in boxplots and normal quantile

plots before using our inference procedures.

The boxplots show pretty clear visual evidence of a di erence in means. The normal

quantile plots show some deviations from linearity, especially for the women. There are also

some indications of extreme values in the data. When considering using the t procedures,

this should give us some pause. But overall it's not terrible, so let's go ahead and use the

t procedures here. The next question is whether we should use the Welch procedure or the

pooled variance version. Since the sample standard deviations are close (7.1 vs 6.8), let's

go with the pooled variance procedure.

Use the pooled variance t procedure for the following problems. Do NOT use

any large sample approximation.

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#9. What is the value of the pooled sample variance?

#10. What is the value of the standard error of the di erence between the sample means?

#11. Construct a 95% con dence interval for the di erence in population means

(male-females). Which one of the following is the appropriate interval?

A) 19:7 4:34

B) 19:7 4:39

C) 19:7 4:44

D) 19:7 4:49

E) 19:7 4:54

#12. Test whether the population mean ratings for men and women are equal. Although

one could make an argument for using a one-sided alternative that the male ratings will be

higher than the female ratings on average, use a two-sided alternative. What are the

appropriate hypotheses?

A) H0 : xM = xF ; Ha : xM 6= xF

B) H0 : xM = xF ; Ha : xM < xF

C) H0 : M = F ; Ha : M 6= F

D) H0 : M = F ; Ha : M > F

E) H0 : M = F ; Ha : M < F

#13. What is the value of the appropriate test statistic?

#14. What is the p-value of the test? We cannot get an exact p-value from the table, but

we can nd an appropriate range of values. Which one of the following is the appropriate

range?

A) p-value <.001

B) .001 < p-value <.002

C) .01 < p-value <.02

D) .05 < p-value <.10

E) .1< p-value

#15. Is there signi cant evidence of a di erence in population means between men and

women at = :01?

A)Yes. B)No.

#16. Which one of the following is the most appropriate conclusion for this hypothesis

test?

A) We can be certain that male guests tend to give higher ratings than female guests at

this hotel.

B) There is very strong evidence that the population mean rating for male guests at this

hotel is greater than the population mean rating for female guests.

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C) There is very strong evidence that the population mean rating for male guests at this

hotel is less than the population mean rating for female guests.

D) There is some evidence that the sample mean rating for male guests at this hotel is

greater than the sample mean rating for female guests at this hotel.

The next series of questions refer to the following information.

Suppose an insurance company is investigating the use of text messsaging by drivers in a

region. As one variable in the study, they are interested in the proportion di erent age

groups who have texted while driving. They conduct a large survey of drivers in the region,

and nd that:

In a random sample of 600 drivers aged 16-19, 372 admitted to texting while driving.

In a random sample of 1500 drivers aged 20-29, 745 admitted to texting while driving.

#17. Calculate a 95% con dence interval for the di erence in population proportions

(teenage - twenties). Which one of the following is the appropriate interval?

A) 0:1233 0:046

B) 0:1233 0:048

C) 0:1233 0:050

D) 0:1233 0:052

E) 0:1233 0:054

Test the null hypothesis that the population proportions of drivers who admit to texting

while driving are equal for the two groups. Use a two-sided alternative.

**Please call the 16-19 group Group 1. Your test statistic should be positive**

#18. What are the appropriate hypotheses?

A) H0 : pteen = ptwenties; Ha : pteen > ptwenties

B) H0 : ^pteen = ^ptwenties; Ha : ^pteen > ^ptwenties

C) H0 : pteen = ptwenties; Ha : pteen 6= ptwenties

D) H0 : ^pteen = ^ptwenties; Ha : ^pteen 6= ^ptwenties

#19. What is the value of the test statistic?

#20. The p-value of the test is closest to which one of the following?

A) .01

B) .05

C) .10

D) .20

E) .50

#21. Which one of the following is the most appropriate conclusion for = :05?

A) There is signi cant evidence that the population proportion for the 16-19 age group is

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less than that of the 20-29 age group.

B) There is not signi cant evidence of a di erence between the population proportions for

the two age groups.

C) There is signi cant evidence that the population proportions for the two age groups are

equal.

D) We can be certain that the sample proportions for the two age groups are equal.

E) There is signi cant evidence that the population proportion for the 16-19 age group is

greater than that of the 20-29 age group.

#22. Suppose we run a hypothesis test and obtain a p-value of .03. Which one of the

following statements is true?

A) The null hypothesis would be rejected at = :10, but not at = :05.

B) The null hypothesis would be rejected at = :05, but not at = :01.

C) The null hypothesis would be rejected at = :01.

D) The null hypothesis would not be rejected at any value of .

Consider the following output for a two-sample inference procedure for the di erence be-

tween population means. The output for both the pooled-variance procedure and Welch's

procedure are given.

Welch Two Sample t-test

data: temp1 and temp2

t = -0.3746, df = 52.842, p-value = 0.7094

alternative hypothesis: true difference in means is not equal to 0

95 percent confidence interval:

-3.699859 2.535360

sample estimates:

mean of x mean of y

19.54801 20.13026

Pooled Variance Two Sample t-test

data: temp1 and temp2

t = -0.3206, df = 53, p-value = 0.7498

alternative hypothesis: true difference in means is not equal to 0

95 percent confidence interval:

-4.224599 3.060100

sample estimates:

mean of x mean of y

19.54801 20.13026

#23. What is the p-value of the test that requires the assumption that the population

variances are equal?

#24. Which of these procedures assumes that we are sampling from normally distributed

populations?

A) Just the pooled-variance t procedure.

B) Just the Welch procedure.

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C) Both procedures.

D) Neither procedure.

#25. Which would be the more appropriate procedure in this case?

A) The pooled variance procedure.

B) Welch's procedure.

C) Impossible to determine with the given information.

#26. Suppose we had 40 pairs of observations of A and B measurements, that resulted in

the following output

Paired t-test

t = -0.3476, df = 39, p-value = 0.73

alternative hypothesis: true difference in means is not equal to 0

95 percent confidence interval:

-0.001649301 0.001165598

sample estimates:

mean of the differences

-0.0002418514

The di erences were taken to be: A readings - B readings.

At = :05, which one of the following is the most appropriate conclusion?

A) There is signi cant evidence that the readings are equal on average.

B) There is signi cant evidence that the A readings are greater than the B readings on

average.

C) There is signi cant evidence that the A readings are less than the B readings on average.

D) There is not signi cant evidence of a di erence in the readings.

E) We can be certain that on average there is a di erence in the A and B readings.

#27. The hydrostatic measurements are less time consuming, and therefore preferable if they provide reasonable readings when compared to the more accurate but time-intensive hydrometer readings. The winery will use the hydrostatic measurements if it can be demon- strated that the mean di erence between the density measurements of the two measure- ments does not exceed .002. Looking at the appropriate values in the output, is there strong evidence that the mean di erence in density measurements exceeds .002? Is there strong evidence that the mean di erence in measurements exceeds .002?

A) Yes, there is strong evidence that the mean di erence exceeds .002.

B) No, there is not strong evidence that the mean di erence exceeds .002.

## [Solved] STAT*2060DE F Assignment #6 | Complete Solution

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