MATH 1342 - Quiz-3
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Stephen F Austin State University *
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Mathematics
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Apr 3, 2024
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MATH 1342 – Introduction to Statistics
Quiz 3
1.
Weight Watchers:
In the article “ Comparison of Atkins, Ornish, Weight Watchers, and Zone Diets for Weight Loss and Heart Disease Risk Reduction”, published in the
Journal of the American Medical Association (Dansinger, et al., Vol. 293, No. 1), 40 people followed a Weight Watchers diet for a year. Their weight losses were summarized by these statistics: x
= 6.6 lbs and s = 10.8 lbs. Use a 1% significance level to evaluate the effectiveness of the Weight Watchers diet. a.
What is the inherent question
of interest here?
b.
What might be a reasonable description of the population
of interest?
c.
What is the relevant sample
here?
d.
What is the random variable
being evaluated here?
e.
What is the population parameter
of interest?
f.
What is this parameter’s corresponding sample statistic
?
g.
What is an appropriate research hypothesis
to consider?
h.
What is the corresponding null hypothesis
?
i.
What is the test statistic
used to test these hypotheses?
j.
What is the null distribution
of this test statistic?
k.
What is the decision rule
that might be used here (use α = 0.01)?
l.
What decision
was made with regard to the null hypothesis?
m.
What is your conclusion based on the available data?
n.
What is your best point estimate
of the average amount of weight lost on the Weight Watchers diet over a year’s time?
o.
Provide a 99% confidence interval
for the average amount of weight lost on the Weight Watchers diet over a year’s time.
p.
Given the results of your evaluation, do you consider the Weight Watchers diet effective? Why or why not?
2.
Breakfast Cereals:
To evaluate the amount of sugar in breakfast cereals, a set of 16
randomly selected cereal types were tested for the amount of sugar in grams per gram of cereal. These results appear among the course Data Files in the Excel file Cereals.xlsx. Use a 5% significance level to test the claim of a cereal industry lobbyist that the mean amount of sugar for all cereals is less than 0.25 grams per gram of cereal.
a.
What is the inherent question
of interest here?
b.
What might be a reasonable description of the population
of interest?
c.
What is the relevant sample
here?
d.
What is the random variable
being evaluated here?
e.
What is the population parameter
of interest?
f.
What is this parameter’s corresponding sample statistic
?
g.
What is an appropriate research hypothesis
to consider?
h.
What is the corresponding null hypothesis
?
i.
What is the test statistic
used to test these hypotheses?
j.
What is the null distribution
of this test statistic?
k.
What is the decision rule
that might be used here (use α = 0.05)?
l.
What decision
was made with regard to the null hypothesis?
m.
What is your conclusion based on the available data?
n.
What is your best point estimate
of the average grams of sugar (per gram of
cereal) in breakfast cereals?
o.
Provide a 95% confidence interval
for the average grams of sugar (per gram
of cereal) in breakfast cereals.
p.
Given the results of your evaluation, do you believe a lobbyist for children’s health and nutrition could reasonably make the claim that the average amount of sugar in breakfast cereals is greater than 0.2 grams per gram of cereal? Why or why not?
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