math 220 project 4
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School
James Madison University *
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Course
220
Subject
Health Science
Date
Feb 20, 2024
Type
Pages
3
Uploaded by mahek92811
Part I (10 Points
)
Dependent Samples T-Test
Comparing two drugs
: Makers of generic drugs must show that they do not differ significantly
from the “reference” drugs that they imitate. One aspect in which drugs might differ is their
extent of absorption in the blood. The following table gives data taken from 20 healthy
nonsmoking male subjects for one pair of drugs. This is a matched pairs design. Numbers 1 to 20
were assigned at random to the subjects. Subjects 1 to 10 received the generic drug first,
followed by the reference drug. Subjects 11 to 20 received the reference drug first, followed by
the generic drug. In all cases, a washout period separated the two drugs so that the first had
disappeared from the blood before the subject took the second. By randomizing the order, we
eliminate the order in which the drugs were administered from being confounded with the
difference in the absorption in the blood.
1. (2 points) Briefly describe the distribution of the differences.
(In SPSS, use RD = Reference Drug, GD = Generic Drug. Create a new variable called
Difference Under Variable View, under Name write Difference. Then back the Data View, click
Transform> Compute Variable. I the Target Variable, write Difference )
-
Mean: -2.35
-
Min: -2030
-
Q1: -674.25
-
Median: -215.5
-
Q3: 478
-
Max: 3046
-
Range: 5076
-
Standard Deviation: 1159.5633
-
IQR: 1152.25
-
Shape: Skewed to the right
1
2. (2 points) Build a 95% CI for the mean difference (Note this is a matched pairs confidence
interval)
95%: (-545.0423, 540.3423)
3. (2 points) (By Hand) Do the drugs differ significantly in the amount absorbed in the blood?
Do a paired t-test to answer the question.
𝐻 𝑁?𝑙𝑙: µ
≠ 0
? =
−2.35−0
1159/ 20
? =− 0. 009
𝑝 = 0. 496 × 2 𝑝 = 0. 993
It fails to reject the H null because the p value (.993) is greater than alpha (0.05). This indicates
that we do not have enough evidence to determine if the drugs differ significantly in the amount
absorbed in the blood.
4. (4 points) Do the drugs differ significantly in the amount absorbed in the blood? Do a paired t-
test to answer the question (This can be done in SPSS by two ways).
? =− 0. 009
𝑝 = 0. 993
We do not reject the null hypothesis since p-value (0.993) is greater than alpha (0.05) meaning
we don’t have enough evidence to make that conclusion that the drug's absorption in blood
differs significantly.
Part II (10 points)
Independent Sample T test
Q1 (5 points):
In an agricultural experiment, the effects of two fertilizers on the production of
2
oranges were measured. Fourteen randomly selected plots of land were treated with fertilizer A,
and 10 randomly selected plots were treated with fertilizer B. The number of pounds harvested of
fruit was measured from each plot. Following are the results.
Assume that the populations are approximately normal.
1. Construct a 90% confidence interval for the difference between the mean yields for the
two types of fertilizer.
90%: (3.0589, 35.9125)
2. Is there a significant difference between the average number of pounds harvested
between the plots that use fertilizer A and those that use fertilizer B? Test using
𝛼
= .05.
It does not reject the null hypothesis because the p-value (0.054) is greater than the alpha (0.05).
This indicates that there is not enough evidence to conclude that there is a significant difference
between the average number of pounds harvested between the plots that use fertilizer A and
those who use fertilizer B.
Q2(5 points) :
British health officials have expressed concern about problems associated with
vitamin D deficiency among certain immigrants. Doctors have conjectured that such a deficiency
could be related to the amount of fiber in a person's diet. An experiment was designed to
compare the vitamin D plasma half-life for two groups of healthy individuals. One group was
placed on a normal diet, whereas the second group was placed on a high-fiber diet. (Based on
data from "Reduced Plasma Half-Lives of Radio-labeled 23(OH)D3 in Subjects Receiving a
High-Fiber Diet," Brit. J. of Nutrit. (1993): 213-216).
Can we conclude the typical half-life is lower for subjects on a high-fiber diet?
Since the p-value (0.003) is less than alpha, it indicates that it rejects the null hypothesis. The
high fiber diet has a significantly lower half-life compared to a normal diet.
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