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Chapter 2 Discrete Random Variables and Probability Distributions
Exercises 2.6
1. If a sample of size 30 is chosen from a binomial distribution with p =
1 2
, and if X denotes the number of successes obtained, find an interval in which 95 of the
values of X will lie.
2. Use your computer algebra system to verify the results in Table 2.6.1 for a. p =
1 2
; n = 36.
b. p =
1 3
; n = 18.
c. p =
1 4
; n = 48.
3. Use your computer algebra system to verify the result in Table 2.6.1 for a. p =
1 2
; n = 10000.
b. p =
1 3
; n = 11250.
c. p =
1 4
; n = 13872.
4. A survey of 300 college students found that 50 are thinking about changing their
majors. Find a 95 confidence interval for the true proportion of college students thinking about changing their majors.
5. A random sample of 1250 voters was asked whether or not they voted in favor
of a school bond issue, and 325 replied that they favored the issue. Find a 95 confidence interval for the true proportion of voters who favor the school bond
issue.
6. Find 90 confidence intervals by constructing a table similar to Table 2.6.1. One
should find that P.¼ − 1:645¦ ≤ X ≤ ¼ + 1:645¦ = 0:90:
7. A newspaper survey of 125 of its subscribers found that 40 of the respondents
knew someone who was killed or injured by a drunk driver. Find a 90 confidence interval for the true proportion of people in the population who know someone
who was killed or injured by a drunk driver.
8. As a project in a probability course, a student discovered that among a random
sample of 80 families, 25 did not have checking accounts. Use this information to construct a 90 confidence interval for the true proportion of families in the
population who do not have checking accounts.
9. A study showed that
1 8
of American workers worked in management or in admin- istration, while
1 27
of Japanese workers worked in management or administration. The study was based on 496 American workers and 810 Japanese workers.
Is it possible that the same proportion of American and Japanese workers are in management or administration and that the apparent differences found by the
2.7 Hypothesis Testing: Binomial Random Variables
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