Researchers collected data on the numbers of hospital admissions resulting from
ID: 3159929 • Letter: R
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: 9 7 12 12 3 6 Friday the 13th: 14 14 15 11 5 12 What are the hypotheses for this test? Let muSubscript dd be the mean of the differences in the numbers of hospital admissions resulting from motor vehicle crashes for the population of all pairs of data. H0: muSubscript dd equals= 0 H1: muSubscript dd not equals 0 Find the value of the test statistic. tequals= nothing
Explanation / Answer
The differences are
5
7
3
-1
2
6
Formulating the null and alternative hypotheses,
Ho: ud = 0
Ha: ud =/ 0
At level of significance = 0.05
As we can see, this is a two tailed test.
Calculating the standard deviation of the differences (third column):
s = 2.757908738
Thus, the standard error of the difference is sD = s/sqrt(n):
sD = 1.125911527
Calculating the mean of the differences (third column):
XD = 3.666666667
As t = [XD - uD]/sD, where uD = the hypothesized difference = 0 , then
t = 3.256620593 [ANSWER, TEST STATISTIC]
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Other details:
As df = n - 1 = 5
Then the critical value of t is
tcrit = +/- 2.570581836
Also, using p values,
p = 0.022529876
As |t| > 2.57, and P < 0.05, WE REJECT THE NULL HYPOTHESIS.
There is significant evidence that that when the 13th day of a month falls on a Friday, the numbers of hospital admissions from motor vehicle crashes are affected.
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