1). Based on the genotypes of parents, offspring are expected to have genotypes
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Question
1). Based on the genotypes of parents, offspring are expected to have genotypes distributed in such a way that 25% have genotypes denoted by AA, 50% have genotypes denoted by Aa, and 25% have genotypes denoted by aa. When 145 offspring are obtained, it is found that 20 of them have AA genotypes, 90 have Aa genotypes, and 35 have aa genotypes. Test the claim that the observed genotype offspring frequencies fit the expected distribution of 25% for AA, 50% for Aa, and 25% for aa. Use a significance level of 0.05.
2). The cholesterol-reducing drug Lipitor consists of atorvastatin calcium and results summarizing headaches as an adverse reaction in clinical tests are given in the table below. Using a 0.05 significance level, test the claim that getting a headache is independent of the amount of atorvastatin used as a treatment. (Hint: Because not all of the expected values are 5 or greater, combine the results for the treatments consisting of 20 mg of atorvastatin and 40 mg of atorvastatin.). Do headaches appear to be a concern for those who are treated with Lipitor?
Placebo
10mg Atorvastatin
20 mg Atorvastatin
40 mg Atorvastatin
80 mg Atorvastatin
Headache
19
47
6
2
6
No Headache
251
816
30
77
88
3). The table below summarizes results from an experiment involving randomly selected subjects who experience some degree of sleeplessness. Some of the subjects were treated with a drug, while others were given a placebo.
Experienced Improvement
Did Not Experience Any Improvement
Treatment Group
10,222
49,875
Placebo Group
10,587
53,252
a). Use the methods of Chapter 10 (Chi-Square) to test for independence between the treatment and placebo group and whether the subject experienced improvement in the degree of sleeplessness. What do you conclude? Does it appear that the treatment is effective? What does the result suggest about the decision to distribute the treatment?
b). Use the methods of Section 8.2 (inference about two proportions) to test the claim that the treatment result in a greater rate of improvement that the rate achieved with a placebo. What do you conclude? Does it appear that the treatment is effective? What does the result suggest about the decision to distribute the treatment.
c). If you are the chief executive officer of a pharmaceutical company and you are given the results in the accompanying table, what should you do? Should you market the treatment? Why or why not?
4. A study is conducted on several species of birds that are similar in nature and share a common environment. The song of each species has a distinctive set of features that permits recognition. One characteristic under investigation is the length of the song in seconds. Three species are studied; the towhee, the common yellowthroat, and the thrasher. The data is given below:
Towhee Common Yellowthroat Brown thrasher
1.11 2.17 .42
1.23 1.85 .93
.91 1.99 .77
.95 1.74 .37
.99 1.54 .50
1.08 1.86 .48
1.18 1.87 .68
1.29 2.04 .62
1.12 1.69 .39
.88 .67
1.34 1.03
.79
Assume normality and equal variances. Test the null hypothesis that the mean song lengths are the same for all three species. If the ANOVA test is rejected, conduct a follow up Bonferoni analysis.
Placebo
10mg Atorvastatin
20 mg Atorvastatin
40 mg Atorvastatin
80 mg Atorvastatin
Headache
19
47
6
2
6
No Headache
251
816
30
77
88
Explanation / Answer
1)
H0: pAA = 0.25, pAa =0.50, pzz = 0.25
H1: At least one of theproportions is not equal to the given claimed value.
Chi^2 = (20-36.25)^2 / 36.25 + (90-72.5)^2 / 72.5 + (35-36.25)^2 / 36.25
= 7.28 + 4.22 + 0.04
= 11.54
df = 3-1 = 2
alpha = 0.05
So, critical value = 5.991
Since the calcualted value of chi-square(11.54) is greater than the critical value of chi-square so we reject the null hypothesis and conclude that the observed genotype offspring frequencies does not fit the expected distribution of 25% forAA, 50% for Aa, and 25% for aa.
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