Chapter 25, Problem 8E

(a)

To determine

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

Answer to Problem 8E

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. And in this case they also examined the number of people admitted to emergency rooms for vehicular accidents on evenings. 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 we have pairs of Fridays in six different months. And the data from adjacent Fridays within a month may be more similar than randomly chosen Fridays.

(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. And in this case they also examined the number of people admitted to emergency rooms for vehicular accidents on evenings. 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 $0.0211$ . So we know that if the P-value is smaller than the significance level, then the null hypothesis is rejected. And thus,

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

This shows that there is evidence that the mean number of admissions to hospitals found on Friday the $13\text{th}$ is more than on the previous Friday.

(c)

To determine

To explain are the assumptions and conditions for inference met.

Answer to Problem 8E

All the assumptions and conditions for inferences are not 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. And in this case they also examined the number of people admitted to emergency rooms for vehicular accidents on evenings. 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 not satisfied as we don't know if these Friday pairs were chosen at random, if not that would affect our conclusion.

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

Normal condition: It is satisfied because the sample size is a little small but nearly Normal condition appears to be met according to its histogram.

Thus, all the conditions for inferences are not met.