Suppose a team of dermatologists are testing the effectiveness of a new skin cre
ID: 3151876 • Letter: S
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.
Conduct a chi-square test for independence at =0.05, using the following null and alternative hypothesis pair:
H0: 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. Based on these results, the statistical decision is:
Reject H0 and conclude that whether or not a patient received skin cream and whether or not that patient's rash got better are dependent. Fail to reject H0 and conclude that whether or not a patient received skin cream and whether or not that patient's rash got better are independent. Reject H0 and conclude that whether or not a patient received skin cream and whether or not that patient's rash got better are independent. Fail to reject H0 and conclude that whether or not a patient received skin cream and whether or not that patient's rash got better are dependent.
c. What are the odds that a patient got better, given that the patient did not receive the skin cream?
Odds =
(round your answer to two decimal places)
d. What are the odds that a patient got better, given that the patient did receive the skin cream?
Odds =
(round your answer to two decimal places)
e. What is the odds ratio that compares the relative odds of getting better for a patient who did not receive the skin vs. a patient who did receive the skin cream?
OR =
(round your answer to two decimal places)
You will now create a 95% confidence interval for this odds ratio. To do this, find the natural log of the odds ratio, i.e. ln(OR). Then find the standard error of ln(OR), then the margin of error for ln(OR), and then use these to make a 95% confidence interval for ln(OR). Finally, convert this to a confidence interval for just the odds ratio rather than for its natural log.
f. ln(OR) =
(round your answer to three decimal places)
g. standard error of ln(OR) =
(round your answer to three decimal places)
h. margin of error for ln(OR) =
(round your answer to three decimal places)
i. 95% confidence interval for ln(OR) = to
(round your answers to three decimal places)
j. 95% confidence interval for OR = to
(round your answers to two decimal places)
k. Based on this confidence interval, what can we say about the association between whether a patient received the skin cream and whether the patient's rash got better?
It appears that the odds of the rash getting better are significantly greater for patients who received the skin cream than for those who did not. It appears that the odds of the rash getting better are significantly greater for patients who did not receive the skin cream than for those who did. It appears that there is not a significant association between whether a patient received the skin cream and whether the rash got better or worse. It is not possible to make an inferential statement about the association between whether a patient received the skin cream and whether the rash got better or worse, using just a confidence interval.
Rash got better Rash got worse Totals Did not receive skin cream 108 21 129 Received skin cream 225 74 299 Totals 333 95 428Explanation / Answer
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.
Rash got better
Rash got worse
Totals
Did not receive skin cream
108
21
129
Received skin cream
225
74
299
Totals
333
95
428
Conduct a chi-square test for independence at =0.05, using the following null and alternative hypothesis pair:
H0: 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.
Chi-Square Test
Observed Frequencies
Column variable
Calculations
Row variable
C1
C2
Total
fo-fe
R1
108
21
129
7.633
-7.633
R2
225
74
299
-7.633
7.633
Total
333
95
428
Expected Frequencies
Column variable
Row variable
C1
C2
Total
(fo-fe)^2/fe
R1
100.367
28.633
129
0.581
2.035
R2
232.633
66.367
299
0.250
0.878
Total
333
95
428
a. The chi-square test statistic is; 3.744
(round your answer to three decimal places)
b. Based on these results, the statistical decision is:
Reject H0 and conclude that whether or not a patient received skin cream and whether or not that patient's rash got better are dependent.
Fail to reject H0 and conclude that whether or not a patient received skin cream and whether or not that patient's rash got better are independent.
Reject H0 and conclude that whether or not a patient received skin cream and whether or not that patient's rash got better are independent.
Fail to reject H0 and conclude that whether or not a patient received skin cream and whether or not that patient's rash got better are dependent.
c. What are the odds that a patient got better, given that the patient did not receive the skin cream?
Odds =5.14
(round your answer to two decimal places)
d. What are the odds that a patient got better, given that the patient did receive the skin cream?
Odds =3.04
(round your answer to two decimal places)
e. What is the odds ratio that compares the relative odds of getting better for a patient who did not receive the skin vs. a patient who did receive the skin cream?
OR =1.69
(round your answer to two decimal places)
You will now create a 95% confidence interval for this odds ratio. To do this, find the natural log of the odds ratio, i.e. ln(OR). Then find the standard error of ln(OR), then the margin of error for ln(OR), and then use these to make a 95% confidence interval for ln(OR). Finally, convert this to a confidence interval for just the odds ratio rather than for its natural log.
f. ln(OR) =0.525
(round your answer to three decimal places)
g. standard error of ln(OR) =0.274
(round your answer to three decimal places)
h. margin of error for ln(OR) =0.537
(round your answer to three decimal places)
i. 95% confidence interval for ln(OR) = -0.012 to 1.062
(round your answers to three decimal places)
j. 95% confidence interval for OR = 0.99 to 2.89
(round your answers to two decimal places)
k. Based on this confidence interval, what can we say about the association between whether a patient received the skin cream and whether the patient's rash got better?
It appears that the odds of the rash getting better are significantly greater for patients who received the skin cream than for those who did not.
It appears that the odds of the rash getting better are significantly greater for patients who did not receive the skin cream than for those who did.
It appears that there is not a significant association between whether a patient received the skin cream and whether the rash got better or worse.
It is not possible to make an inferential statement about the association between whether a patient received the skin cream and whether the rash got better or worse, using just a confidence interval.
Rash got better
Rash got worse
Totals
Did not receive skin cream
108
21
129
Received skin cream
225
74
299
Totals
333
95
428
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