Suppose a team of dermatologists are testing the effectiveness of a new skin cre

Question

Suppose a team of dermatologists are testing the effectiveness of a new skin cream designed to treat rashes, but which they suspect may also make rashes worse in some patients. They run an experiment using patients with skin rashes, in which some are given the cream and some are not. For each patient, they record whether the patient's rash got better or worse. The results are in the table below Did not receive skin cream Received skin cream Totals Rash got better Rash got worse Totals 18 125 73 298 423 107 225 332 91 Conduct a chi-square test for independence at ?=0.05, using the following null and alternative hypothesis pair: Ho: whether or not a patient received skin cream and whether or not that patient's rash got better are independent. Ha: whether or not a patient received skin cream and whether or not that patient's rash got better are dependent note: For intermediate calculations, use three decimal places of precision a. The chi-square test statistic is: (round your answer to three decimal places) b. The p-value for this test is: (round your answer to four decimal places) C. Based on these results, the statistical decision is: O Reject Ho and conclude that whether or not a patient received skin cream and whether or not that patient's rash got better are dependent O Fail to reject Ho and conclude that whether or not a patient received skin cream and whether or not that patient's rash got better are independent O Reject Ho and conclude that whether or not a patient received skin cream and whether or not that patient's rash got better are independent. O Fail to reject Ho and conclude that whether or not a patient received skin cream and whether or not that patient's rash got better are dependent.

Explanation / Answer

Ans:

a)

Test statistic:

Chi square=5.317

b)df=(2-1)*(2-1)=1

p-value=CHIDIST(5.317,1)=0.0211

c)

As,p-value<0.05, We reject the null hypothesis.

Reject H0 and conclude that whether or not a patient recieved skin cream and whether or not that patient rach got batter are dependent.

(first option is correct)

Observed(fo) Better worse Total did not received 107 18 125 receive 225 73 298 Total 332 91 423 Expected(fe) Better worse Total did not received 98.109 26.891 125 receive 233.891 64.109 298 Total 332 91 423 Chi square=(fo-fe)^2/fe Better worse Total did not received 0.806 2.940 3.746 receive 0.338 1.233 1.571 Total 1.144 4.173 5.317

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