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. Construct a 95% confidence interval estimate of the mean of the population of differences between hospital admissions on days that are Friday the 6th of a month and days that are Friday the 13th of a month. Use the confidence interval 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 {9, 6, 11, 11, 3, 5)

Friday the 13th {13,12,14,10,4,12)

1. What are the hypothesis for this test?

2. Find the value of the test statistic.

3. Identify critical values.

4. State the result of the test

Please explain.

Answer 1

	Friday the 6th	Friday the 13th	Diff
	9	13	-4
	6	12	-6
	11	14	-3
	11	10	1
	3	4	-1
	5	12	-7
Mean			-3.33
Std Dev			3.01

Alpha = 0.05

ZCritical = 1.96

95% CI for difference of means = -3.33 +/- 1.96*(3.01/6^1/2) ={-5.74, -0.92}

Null and Alternate Hypothesis

H₀: µ_D = 0

H_a: µ_D <> 0

Test Statistic

t = -3.33/(3.01/6^1/2) = -2.71

Critical Values = -2.571, 2.571

Result

Since the test statistic is less than -2.571, we reject the null hypothesis

Conclusion

There is difference in hospital admissions if it is Friday 13th