Homework 3 (20 points)
STAT 110
Name(s) ___SOLUTION__
Due: Wednesday, September 26th by 4pm
1. Determine the appropriate null and alternative hypotheses for the each of the scenarios given
below. Please use symbol notation.
a. Becker et al. (International Journal of Eating Disorders 2003) conducted a study using a
sample of 50 ethnic Fijian women. The women completed a self-report questionnaire
on dieting and attitudes toward body shape and change. The researchers found that
five of the respondents reported at least weekly episodes of binge eating during the
previous 6 months. (2 points)
Research Question – Is there evidence to conclude that less than 20 percent of
the population of Fijian women engage in at least weekly episodes of binge
eating?
H0: p ≥ 0.20
Ha: p < 0.20
b. A study was designed to determine whether dogs can be trained to identify urine
specimens from individuals with bladder cancer. Dogs were first trained to discriminate
urine samples from patients with bladder cancer or with other conditions. After the
training was completed, the dogs had to pick one of seven new urine specimens. Each
time, only one of the seven urine specimens came from a patient with bladder cancer.
Out of 54 trials, the dogs identified the correct urine specimen 22 times. (2 points)
Research Question – Are dogs able to identify urine specimens from patients
with bladder cancer?
H0: p ≤ 0.14
Ha: p > 0.14
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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. Construct a 99% confidence interval by hand for the proportion of mixed progeny.
(3 points)
n = 100
pˆ =
11
= 0.11
100
z = 2.58
2(100)(0.11) + 2.582 2.58 2.582 + 4(100)(0.11)(0.89)
±
2 100 + 2.582 
2 100 + 2.582 
28.66
17.46
±
 0.13 ± 0.08  0.05 ≤ p ≤ 0.21
213.31 213.31
b. Interpret the 99% confidence interval constructed in part a. (3 points)
99% confident the true proportion of red-eyed fruit flies crossed with whiteeyed mutants with mixed progeny is between 0.05 and 0.21.
c. Using JMP, verify the 99% confidence interval you constructed in part a. Make sure to
provide your JMP output or a detailed sketch of the output below. (2 points)
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3. An experiment on the side effects of pain relievers assigned arthritis patients to take one of
several over-the-counter pain medications. Of the 440 patients who took one brand of pain
reliever, 23 suffered “adverse symptoms.”
a. Construct a 90% confidence interval by hand for the proportion of arthritis patients who
suffered “adverse symptoms” from taking the over-the-counter pain medication.
(3 points)
n = 440
pˆ =
23
= 0.05
440
z = 1.645
2(440)(0.05) + 1.6452 1.645 1.6452 + 4(440)(0.05)(0.95)
±
2  440 + 1.6452 
2  440 + 1.6452 
46.71
15.28
±
 0.05 ± 0.02  0.03 ≤ p ≤ 0.07
885.41 885.41
b. Interpret the 90% confidence interval constructed in part a. (3 points)
90% confident the true proportion of arthritis patients who suffered “adverse
symptoms” from taking the over-the-counter pain medication is between 0.03
and 0.07.
c. Using JMP, verify the 90% confidence interval you constructed in part a. Make sure to
provide your JMP output or a detailed sketch of the output below. (2 points)
3