Lab 8
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ReMA | Quantitative Foundations | Fall 2023
Lab 8
11/17/2023
1.
A group of researchers is interested in seeing if participation in a nutritional program is likely to
improve outcomes for expecting mothers who are at high risk of giving birth to a low birthweight baby.
They plan a cohort study that will enroll low-income pregnant women living in Mumbai, India, where
some pregnant women have signed up for a nutritional program and others have not. This study design
gives the researchers flexibility to assess several outcomes of interest. Help the researchers determine
the appropriate statistical test for each of the following questions. For each scenario, state the
appropriate test and explain why it is the appropriate test.
a.
Is there a difference in mean birthweight (in grams) between babies born to mothers who sign
up for the nutritional program and babies born to mothers who do not sign up for the
nutritional program?
b.
Is there an association between participation in the nutritional program and giving birth to a
normal birthweight baby (2,500 g or more)?
c.
Does the average birthweight among women in Mumbai who participate in nutrition programs
during pregnancy differ from the Indian national mean birthweight of 2,552 g?
d.
Some mothers are signed up for a personalized nutritional program, some are signed up for a
group nutritional program, and some are signed up for a control program about how to care for
a newborn baby. Is there a difference in birthweight (in grams) between babies born to mothers
in in either of these groups?
e.
Among those attending the nutritional program, Is there an association between the amount of
time a pregnant woman in Mumbai spends attending a nutritional program (in minutes) and a
baby’s birthweight?
1
2.
You are asked to assess whether “chance” is a reasonable explanation for any association between type
of nutritional program (none, individual nutritional program, or group nutritional program) and mean
birthweight. You are given the following data, where the birthweight variable is measured continuously
in grams and the program variable is coded as 0 = no nutritional program, 1 = individual nutritional
program, and 2 = group nutritional program.
a)
Conduct the appropriate hypothesis using the steps outlined below. Assume
α
=
0.05
.
i.
State
the null and alternative hypotheses.
ii.
Convert
the data to the appropriate test statistic.
iii.
Compare
the test statistic to the critical value of the appropriate known distribution and
calculate the corresponding p-value range.
b)
Your colleague says this result means that babies born to mothers in Mumbai who enroll in a group
nutritional program during pregnancy have significantly different birthweights than those in an
individual or control program. Do you agree? Why or why not?
2
c)
You decide to conduct an additional test and produce the following output. What question can be
answered using this output?
d)
Assuming
α
=
0.05
, what is the answer to the question from part c)? Explain your reasoning.
3.
Researchers at the WHO are interested in studying the effects of antibiotic use on obesity among adult
men. Previous research suggests that the mean BMI for adult men is 30.0 kg/m
2
with a standard
deviation of 4.73 kg/m
2
. Pilot data suggest that the true mean difference in BMI between adult men
who have taken antibiotics in the past 5 years compared to those who have not taken antibiotics in the
past 5 years is about 5 kg/m
2
.
a)
Assuming an alpha level of 0.05, if the researchers plan to recruit 25 adult men who have taken
antibiotics in the past 5 years and 25 adult men who have not taken antibiotics in the past 5 years,
what is their power to reject the null hypothesis that there is no association between antibiotic use
and BMI under the design alternative hypothesis specified in the STATA output? Use the STATA
output below to answer your question.
power twomeans 30 35, sd(4.73) n(50)
Estimated power for a two-sample means test
t test assuming sd1 = sd2 = sd
Ho: m2 = m1
versus
Ha: m2 != m1
Study parameters:
3
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alpha =
0.0500
N =
50
N per group =
25
delta =
5.0000
m1 =
30.0000
m2 =
35.0000
sd =
4.7300
Estimated power:
power =
0.9556
b)
How would we expect the power to change from part a) if a new pilot study suggests that the true
mean difference in BMI between adult men who have taken antibiotics in the past 5 years
compared to those who have not taken antibiotics in the past 5 years is about 2.5 kg/m
2
, holding all
else constant?
c)
How would we expect the power to change from part a) if the WHO received additional funds that
allow them to recruit a larger sample of 40 adult men who have taken antibiotics and 40 adults who
have not taken antibiotics, holding all else constant?
d)
How would we expect the power to change from part a) if the WHO decides to raise the alpha level
to 0.10, holding all else constant?
e)
Assuming alpha it set to 0.05, the standard deviation is 4.73, and the true mean difference between
the groups is 5 kg/m
2
, how many participants would you need per group to achieve a power of
90%? Use hand calculations to answer this question.
4