STAT412
Homework 5
Due Friday, March 11
Instructions: For problems 1-4, use traditional approach and p-value approach to hypothesis testing. Show all
of the steps of the hypothesis test for each approach. Statistical software can be used for this assignment.
1. An experimenter wished to determine whether there is a relationship between hair color and eye color. One
hundred people were randomly selected and the eyes and hair of each person were judged to be light or dark. A
summary of the number of people in each of the four categories is shown in the table. Do the data provide
sufficient evidence to indicate a relationship between eye and hair color? Conduct hypothesis test using =.01.
Light Hair
31
14
Light Eyes
Dark Eyes
Dark Hair
21
34
2. In a sample of 88 adults selected randomly from one town, it is found that 6 of them have been exposed to a
particular strain of the flu. At the 0.01 significance level, test the claim that the proportion of all adults in the
town that have been exposed to this strain of the flue differs from the nationwide proportion of .08. Use =.05.
3. According to a geneticist’s theory, a crossing of red and white snapdragons should produce offspring that are
25% red, 50% pink, and 25% white. An experiment conducted to test the theory produced 30 red, 78 pink, and
36 white offspring in 144 crossings. Conduct hypothesis test using =.05.
4. Two antibiotics are to be compared. Cultures from 387 out 450 patients treated with antibiotic A showed
antibacterial activity while cultures from 278 out of 350 patients treated with antibiotic B showed antibacterial
activity. Is there sufficient evidence to conclude a difference in the proportion of active cultures for the two
antibiotics? Use =.05.
5. A survey of 865 voters in one state reveals that 408 favor approval of an issue before the legislature.
Construct a 95% confidence interval for the proportion of all voters in the state who favor approval.
6. Consider the accompanying 2  3 table displaying the sample proportions that fell in the various
combinations of categories (e.g., 13% of those in the sample were in the first category of both factors).
1
2
1
.13
.07
2
.19
.11
3
.28
.22
What is the smallest sample size n for which these observed proportions would result in rejection of the
independence hypothesis? Use =.01.
7. A hypothesis test will be performed to test the claim that a population proportion is less than 0.70. A sample
size of 400 and significance level of 0.05 will be used. If = 0.64, find the probability of making a type II error,
β.