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)

Answer 1

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