Over the past semester, you\'ve collected the following data on the time it take

Question

Over the past semester, you've collected the following data on the time it takes you to get to school by bus and by car:

• Bus:(15,10,7,13,14,9,8,12,15,10,13,13,8,10,12,11,14,11,9,12) • Car:(5,8,7,6,9,12,11,10,9,6,8,10,13,12,9,11,10,7)

You want to know if there's a difference in the time it takes you to get to school by bus and by car.

**How is the interval computed on a calculator different from the interval computed by hand? Why is it different? In this case, would you come to a different conclusion for the hypothesis H0 : (u-u2) =? ? 0 if you used the confidence interval generated by the calculator? (1 point)

Explanation / Answer

We can solve this using the open source statisitical package R , the complete R snippet is as follows

Bus<- c(15,10,7,13,14,9,8,12,15,10,13,13,8,10,12,11,14,11,9,12)
Car<- c(5,8,7,6,9,12,11,10,9,6,8,10,13,12,9,11,10,7)

## per form a t test
t.test(Bus,Car)

The results are

t.test(Bus,Car)

Welch Two Sample t-test

data: Bus and Car

t = 2.9588, df = 35.844, p-value = 0.005442 ## as the p value is less than 0.05 , hence we reject null hypothesis in favor of alternate hypothesis to conclude that the difference is signficant

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

95 percent confidence interval:

0.7057921 3.7830968 ## as we see that the confidence interval does not include zero , hence we can conclude that the mean values for bus and car are statistically different

sample estimates:

mean of x mean of y

11.300000 9.055556

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