#1. A drug company asserts that its course of treatment, will, on average, reduc
ID: 1179598 • Letter: #
Question
#1. A drug company asserts that its course of treatment, will, on average, reduce a person's cholestrol level by 0.8 mmol/L. A researcher undertakes a trial with a sample of 30 individuals. What should he report if he obtains the following results:
(a) A mean increase of 0.6 units, with standard error 0.2 units;
(b) A mean decrease of 0.4 units, with standard error 0.2 units;
(c) A mean increase of 0.4 units, with standard error 0.2 units?
*Note there are two null hypotheses to consider here: a) The drug company's claim is true. b) The drug has no effect. *
#2. In the previous question, a researcher was evaluating the assertion of a drug company that its course of treatment will, on average, reduce a person's cholestrol level by 0.8 mmol/L. Explain whether he might have been justified in performing one-sided tests in cases (a) - (c), and determine whether his conclusions would have been different.
Explanation / Answer
The drug company's claim is true Ho : ?1 - ?2 = -0.8
The drug has no effect. Hio : ?1 - ?2 = 0
t = [ (x1 - x2) - d ] / SE
C.I is 95%, alpha is 5%
(a) A mean increase of 0.6 units, with standard error 0.2 units;
to = (0.6+0.8)/0.2 = 7
to > talpha/2, 28, Ho is rejected. Hence, the drug company's claim is not true.
to = (0.6)/0.2 = 3
to > talpha/2, 28, Hio is rejected. Hence, the drug has some effect.
(b) A mean decrease of 0.4 units, with standard error 0.2 units;
to = (-0.4+0.8)/0.2 = 2
to < talpha/2, 28, Ho is failed to be rejected. Hence, the drug company's claim is true.
to = (-.4)/0.2 = -2
to < talpha/2, 28, Hio is failed to be rejected. Hence, the drug has no effect.
(c) A mean increase of 0.4 units, with standard error 0.2 units.
to = (0.4+0.8)/0.2 = 6
to > talpha/2, 28, Ho is rejected. Hence,the drug company's claim is not true.
to = (0.4)/0.2 = 2
to < talpha/2, 28, Hio is failed to be rejected. Hence, the drug has no effect.
2)
Since the objective of the study was to find whether the company's statement was true and the one tailed test would have been possible considering the hypothesis if the drug was less effective or equal to the claim as if it were more effective it was a better thing, and hence one tailed test could have been justified on this ground. Similarily for the second hypothesis as well, whether there was no effect or the effect was positive could have been considered for the one tailed test for the same reason.
at 95% probabililty, and 28 dof
one tailed t stat = 1.701
two tailed t stat = 2.048
Hence the results would have been different and the hypothesis not rejected above would have also been rejeced.
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