Chapter 25, Problem 7E

(a)

To determine

To explain which of the tests is appropriate for these data.

Answer to Problem 7E

Paired t -test is appropriate.

Explanation of Solution

In the question researchers in Britain examined how Friday the $13\text{th}$ affects human behaviour. In which, one question was whether people wants to stay at home more on Friday the $13\text{th}$ . And the data were collected for the number of cars passing junctions for consecutive Fridays for five different periods. Thus, for this experiment conducted, two tests are conducted. First is paired t -test and the other one is two-sample t -test. The software output of the two tests are also given. Thus, we will use the paired t -test if the two groups contain the same subjects or pairs of related subjects and we will use two-sample t -test if the subjects of the two groups are not related. Thus, in this case, paired t -test is appropriate for these data because both groups will contain the same subjects as the dates will be in the same month.

(b)

To determine

To state your conclusion using the test you selected.

Explanation of Solution

In the question researchers in Britain examined how Friday the $13\text{th}$ affects human behaviour. In which, one question was whether people wants to stay at home more on Friday the $13\text{th}$ . And the data were collected for the number of cars passing junctions for consecutive Fridays for five different periods. Thus, for this experiment conducted, two tests are conducted. First is paired t -test and the other one is two-sample t -test. The software output of the two tests are also given. As, for these data, paired t -test is appropriate and the P-value is given for it as $0.0212$ . So we know that if the P-value is smaller than the significance level, then the null hypothesis is rejected. And thus,

  $P<0.05\Rightarrow \text{ Reject }{H}_0$

Thus, we conclude that there is sufficient evidence to support the claim of a decrease.

(c)

To determine

To explain are the assumptions and conditions for inference met.

Answer to Problem 7E

All the assumptions and conditions for inferences are met.

Explanation of Solution

In the question researchers in Britain examined how Friday the $13\text{th}$ affects human behaviour. In which, one question was whether people wants to stay at home more on Friday the $13\text{th}$ . And the data were collected for the number of cars passing junctions for consecutive Fridays for five different periods. Thus, for this experiment conducted, two tests are conducted. First is paired t -test and the other one is two-sample t -test. The software output of the two tests are also given. And for these data, paired t -test is appropriate. Thus, we will check the assumptions and conditions for inference as:

Random condition: It is satisfied as assuming that the Fridays (the $\text{6th and the 13th}$ ) were randomly selected.

Independent condition: It is satisfied because the Fridays are in difference months/years.

Normal condition: It is satisfied because the normal quantile plot is approximately linear.

Thus, all the conditions for inferences are met.