Homework 3 (21 points)
STAT 305
Name(s) _______________________________
Due: Wednesday, September 26 th 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? 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?
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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 90% confidence interval by hand for the proportion of mixed progeny.
(3 points) b.
Interpret the 90% confidence interval constructed in part a. (3 points) 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)
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3.
The offspring produced by a cross between two given types of plants can be any of the three genotypes denoted by A, B, and C. A theoretical model of gene inheritance suggests that the offspring of types A, B, and C should be in the ratio of 1:2:1. For experimental verification, 100 plants are bred by crossing the two given types. Their genetic classifications are recorded in the table below.
Genotype
Observed Frequency
A
18
B
55
C
27
Total
100
Research Question – Do the offspring fit the theoretical model of gene
inheritance for these two types of plants? a.
Set up the null and alternative hypotheses for this scenario. (2 points) b.
Find the expected counts which would be used in the computation of the Chi-square test statistic. Make sure to show how you computed the expected counts. (2 points)
Genotype
Expected Count
A B C Total
100 c.
Using JMP, find the test statistic and p-value for this test. Paste or provide a detailed sketch of the appropriate JMP below. (2 points) d.
Based on the p-value found in part c, does this study provide evidence the offspring fit the theoretical model of gene inheritance for these two types of plants? Explain.
(3 points)
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