Question: To compare the average number of hours Canadians and Americans spend commuting per week, suppose a researcher collected simple random samples of 50 Canadian adults and 50 American adults. R output for their reported weekly commuting times (in hours) are given below.

( Graph attached to email )

> summary(CAN)

Min. 1st Qu. Median Mean  3rd   Qu. Max.

0.00  3.00    4.00  4.86  7.00  11.00

> summary(US)

Min. 1st Qu. Median Mean 3rd Qu. Max.

1.0   4.0     4.0   4.4   5.0    7.0

> sd(CAN)

[1] 2.828499

> sd(US)

[1] 1.277753

Use the information on the previous page to answer parts a. and b. of this question.

1. Three different procedures were run using R on this data set. The resulting output is shown below in i ‐ iii. Note that they all give different results, even though they are based on the same data. Answer the following questions for each of set of output (i, ii and iii):

• What procedure is this output for?

• Is this procedure appropriate to address the question of interest (i.e., to compare the average number of hours Canadians and Americans spend commuting per week)? Why or why not?

1. > t.test(Commute~Country,paired=TRUE)

Paired t-test

data: Commute by Country

t = 0.94184, df = 49, p-value = 0.3509

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

95 percent confidence interval:

-0.5214852 1.4414852

sample estimates:

mean of the differences

0.46

ii. > t.test(Commute~Country)

Welch Two Sample t-test

data: Commute by Country

t = 1.048, df = 68.199, p-value = 0.2983

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

95 percent confidence interval:

-0.4158286 1.3358286

sample estimates:

mean in group CAN mean in group US

4.86 4.40

iii. > t.test(Commute~Country,var.equal=TRUE)

Two Sample t-test

data: Commute by Country

t = 1.048, df = 98, p-value = 0.2972

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

95 percent confidence interval:

-0.4110461 1.3310461

sample estimates:

mean in group CAN mean in group US

4.86 4.40

b. Use the R output (from part a.) for the most appropriate procedure in this situation to compare the average number of hours

Canadians and Americans spend commuting per week. Be sure to write down the procedure you select, provide a conclusion in the context of this study and show all your steps.

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Solution: The downloadable solution consists of 4 pages
Deliverable: Word Document