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# Hypothesis Test

Friday the 13th, Part I. In the early 1990’s, researchers in the UK collected data on traffic flow, number of shoppers, and traffic accident related emergency room admissions on Friday the 13th and the previous Friday, Friday the 6th. The histograms below show the distribution of number of cars passing by a specific intersection on Friday the 6th and Friday the 13th for many such date pairs. Also given are some sample statistics, where the difference is the number of cars on the 6th minus the number of cars on the 13th.19

Friday the 6th

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120000 130000 140000

0

1

2

3

4

Friday the 13th

120000 130000 140000

0

1

2

3

Difference

0 2000 4000

0

1

2

3

4

5

6th 13th Diff.

x̄ 128,385 126,550 1,835 s 7,259 7,664 1,176 n 10 10 10

(a) Are there any underlying structures in these data that should be considered in an analysis? Explain.

(b) What are the hypotheses for evaluating whether the number of people out on Friday the 6th is different than the number out on Friday the 13th?

(c) Check conditions to carry out the hypothesis test from part (b).

(d) Calculate the test statistic and the p-value.

(e) What is the conclusion of the hypothesis test?

(f) Interpret the p-value in this context.

(g) What type of error might have been made in the conclusion of your test? Explain.

Friday the 13th, Part II. The Friday the 13th study reported in Exercise 7.23 also provides data on traffic accident related emergency room admissions. The distributions of these counts from Friday the 6th

and Friday the 13th are shown below for six such paired dates along with summary statistics. You may assume that conditions for inference are met.

Friday the 6th 5 10

0

1

2

Friday the 13th 5 10

0

1

2

Difference −5 0

0

1

2

6th 13th diff

Mean 7.5 10.83 -3.33 SD 3.33 3.6 3.01 n 6 6 6

(a) Conduct a hypothesis test to evaluate if there is a difference between the average numbers of traffic accident related emergency room admissions between Friday the 6th and Friday the 13th.

(b) Calculate a 95% confidence interval for the difference between the average numbers of traffic accident related emergency room admissions between Friday the 6th and Friday the 13th.

(c) The conclusion of the original study states, “Friday 13th is unlucky for some. The risk of hospital admission as a result of a transport accident may be increased by as much as 52%. Staying at home is recommended.” Do you agree with this statement? Explain your reasoning.

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