Homework 2 (27 points)
STAT 110
Name(s) ___SOLUTION_______
Due: Thursday, February 14th by 4pm
1. A Pew Research Center survey was given to 1931 randomly selected adult internet users and
found that 1120 of them said the internet has helped them in some way with obtaining health
information.
a. Using JMP, construct a 99% confidence interval for the true proportion of adult internet
users who said the internet has helped them in some way with obtaining health
information. Give the bounds of the interval below. (2 point)
__0.55__ ≤ p ≤ ___0.61__
b. Interpret the 99% confidence interval found in part a. (3 points)
99% confident the true proportion of adult internet users that say the internet
has helped them in some way with obtaining health information is between
0.55 and 0.61.
2. Wild-type fruit flies have red eyes, but a recessive mutation produces white-eyed individuals. A
researcher wants to assess the frequency of heterozygous individuals from among red-eyed fruit
flies. A heterozygous red-eyed fly crossed with a white-eyed mutant will have a mixed progeny.
Of the 100 red-eyed fruit flies crossed with white-eyed mutants, 11 produced a mixed progeny.
a. Using JMP, construct a 90% confidence interval for the true proportion of mixed
progeny. (2 points)
___0.07__ ≤ p ≤ ___0.17__
b. Interpret the 90% confidence interval found in part a. (3 points)
99% confident the true proportion of mixed progeny fruit flies is between 0.07
and 0.17.
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3. Time Magazine did a report on a 1994 survey asking adult American Catholics “Do you favor
allowing women to be priests?” A random sample of 507 adult American Catholics was taken
and 279 said they were in favor of allowing women to be priests.
Research Question – Is there evidence the majority of adult American Catholics is in
favor of allowing women to be priests?
a. Define the population of interest. (1 point)
b. Identify the sample. (1 point)
All adult American Catholics
507 adult American Catholics
c. Define the variable of interest. (1 point)
Opinion
d. Identify the parameter of interest. (1 point)
p = true proportion of all adult American Catholics who favor allowing women to be
priests
279
e. Identify the statistic. (1 point) pˆ =
= 0.55
507
f. Describe in context how the Binomial Distribution can be used to model this scenario.
(4 points)
1. n = 507 American Catholics
2. 2 outcomes – favor allowing women to be priests, don’t favor allowing
women to be priests
3. P(favor allowing women to be priests) = 0.50 for each American Catholic
4. Adult American Catholics are independent of one another
g. Determine the appropriate null and alternative hypotheses that would be used to test
the research question of interest. (3 points)
H0: p ≤ 0.50
Ha: p > 0.50
h. Using the BinomialProbabilities.jmp file on the course website, calculate the p-value for
this study. (2 points)
p-value = 0.0131
i.
Using the p-value from part h, what conclusion can be made regarding the research
question? (3 points)
There is statistically significant evidence (since 0.0131 < 0.05) that the majority of
adult American Catholics favor allowing women to be priests.
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