stat hw

Stat 20 Homework 11
Please do this assignment in R Markdown and submit the knitted document.

1. Ch 28 A5: Suppose that a die is rolled 600 times with the following results. Make a � -test
of the null hypothesis that the die is fair.

2. Ch 28 C3: The table below shows the distribution of marital status by sex for persons age
25- 34 in Wyoming. Question: Are the distributions really different for men and women?
You may assume the data are from a simple random sample of 299 persons, of whom 143
were men and 156 were women. Make a � -test of the null hypothesis that marital status
and gender are independent. If they are not independent, who are the women marrying?

3. Ch 28 Rev 2: As part of a study on the selection of grand juries in Alameda county, the
educational level of grand jurors was compared with the county distribution. Could a
simple random sample of 62 people from the county show a distribution of educational
level so different from the county-wide one? Do the appropriate hypothesis test.

χ 2

Value Observed count

1 90

2 110

3 100

4 80

5 120

6 100

χ 2

Men Women

Never married 31.5% 19.2%

Married 60.1% 67.3%

Widowed, divorced,
separated

8.4% 13.5%

Education Level County Number of Jurors

Elementary 28.4% 1

Secondary 48.5% 10

Some college 11.9% 16

College degree 11.2% 35

Total 100% 62

4. Ch 28 Rev 9: Each respondent in the Current Population Survey of March 2005 can be
classified by age and marital status. The table below shows results (counts) for the women
who were age 20-29 in Montana. Read questions i) and ii), then answer a) and b).

i) Women of different ages seem to have different distributions of marital status. Or is
this just chance variation?

ii) If the difference is real, what accounts for it?

a) Can you answer these questions with the information given? If so, answer them. If not,
why not?

b) Can you answer these questions if the data in the table resulted from a simple random
sample of women age 20–29 in Montana? If so, answer them. If not, why not?

5. Ch 29 B1: One hundred investigators each set out to test a different null hypothesis.
Unknown to them, all the null hypotheses happen to be true. Investigator #1 gets a p-
value of 58%, plotted in the graph below as the point (1, 58). Investigator #2 gets a p-
value of 42%, plotted as (2, 42). And so forth. The 5%-line is shown. (The y axis should
really be labeled p-value.)

a) How many investigators should get a statistically significant result?

b) How many do?

c) How many should get a result which is highly significant?

Marital Status Age 20-24 Age 25-29

Never Married 46 21

Married 17 32

Widowed, Divorced, Separated 1 6

6. Ch 29 B8: An investigator has independent samples from box A and from box B. Her null
hypothesis says that the two boxes have the same average. She looks at the difference

average of sample from A – average of sample from B

The two-sample z-test gives z� 1.79. Is the difference statistically significant if the
alternative hypothesis says that the average of box A is…

a) bigger than the average of box B?

b) smaller than the average of box B?

c) different from the average of box B?

6. Ch 29 D1: One term, there were 600 students who took the final in 2 at the
University of California, Berkeley. The average score was 65, and the SD was 20 points. At
the beginning of the next academic year, the 25 teaching assistants assigned to the
course took exactly the same test. The TAs averaged 72, and their SD was 20 points too.
Did the TAs do significantly better than the students? Tf appropriate, make a two-sample
z-test. If this isn’t appropriate, explain why not.

7. In employment discrimination cases, some courts have held that there is proof of
discrimination when the percentage of blacks among a firm’s employees is lower than the
percentage of blacks in the surrounding geographical region, provided the difference is
“statistically significant” by the z-test. Suppose that in one city, 10% of the people are
black. Suppose too that every firm in the city hires employees by a process which, as far as
race is concerned, is equivalent to simple random sampling. Would any of these firms
ever be found guilty of discrimination by the z-test? Explain briefly.

8. Ch 29 Rev 9bc (relabeled a and b) : In 1970, 36% of first-year college students thought
that “being very well off financially is very important or essential.” By 2000, the percentage
had increased to 74%. These percentages are based on nationwide multistage cluster
samples.

a) Does it make sense to ask if the difference is statistically significant? Can you answer
on the basis of the information given?

b) Repeat a), assuming the percentages are based on independent simple random
samples of 1,000 first-year college students drawn each year.

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