Question

Researchers collected data on the numbers of hospital admissions resulting from motor vehicle​ crashes, and results are given below for Fridays on the 6th of a month and Fridays on the following 13th of the same month. Use a 0.05 significance level to test the claim that when the 13th day of a month falls on a​ Friday, the numbers of hospital admissions from motor vehicle crashes are not affected.

Friday the 6th:   Friday the 13th:
10 14
6 12
11 13
11 10
4 6
4 10

1. What are the hypotheses for this​ test?

Let μd be the________________________________ in the numbers of hospital admissions resulting from motor vehicle crashes for the population of all pairs of data.

H0​: μd ____ 0

H1​: μd _____ 0

2. Find the value of the test statistic.

t = ????

​(Round to three decimal places as​ needed.)

3. Identify the critical​ value(s). Select the correct choice below and fill the answer box within your choice.

​(Round to three decimal places as​ needed.)

A. The critical values are t= +/-____

B. The critical value is t=______.

4. State the result of the test. Choose the correct answer below.

A. There is sufficient evidence to warrant rejection of the claim of no effect. Hospital admissions appear to be affected.

B. There is not sufficient evidence to warrant rejection of the claim of no effect. Hospital admissions do not appear to be affected.

C. There is not sufficient evidence to warrant rejection of the claim of no effect. Hospital admissions appear to be affected.

D. There is sufficient evidence to warrant rejection of the claim of no effect. Hospital admissions do not appear to be affected.

Answer 1

The statistical software output for this problem is:

Hence,

1) Mean of differences

Hypotheses:

H₀ : μ_D = 0
H_A : μ_D ≠ 0

2) t = -2.858

3) Option A; t = +/- 2.571

4) There is sufficient evidence to warrant rejection of the claim of no effect. Hospital admissions appear to be affected. Option A is correct.