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Chapter 7: Q. 5 (page 462)
Suppose we roll a fair die four times. The probability that a occurs on exactly one of the rolls is
(a)
(b)
(c)
(d)
(e)
The probability that a occurs on exactly one of the rolls is option (c) .
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The Harvard College Alcohol Study finds that of college students support efforts to "crack down on underage drinking." The study took a random sample of almost students, so the population proportion who support a crackdown is close to The administration of a local college surveys an SRS of students and finds that support a crackdown on underage drinking.
(a) Suppose that the proportion of all students attending this college who support a crackdown is , the same as the national proportion. What is the probability that the proportion in an SRS of students is as small as or smaller than the result of the administration鈥檚 sample? Follow the four-step process.
(b) A writer in the college鈥檚 student paper says that 鈥渟upport for a crackdown is lower at our school than nationally.鈥� Write a short letter to the editor explaining why the survey does not support this conclusion
Scooping beads A statistics teacher fills a large container with white and red beads and then mixes the beads thoroughly. She then has her students take repeated SRSs of beads from the container. After many SRSs, the values of the sample proportion p藛 of red beads are approximated well by a Normal distribution with mean of and standard deviation of .
(a) What is the population? Describe the population distribution. (b) Describe the sampling distribution of . How is it different from the population distribution?
ACT scores The composite scores of individual students on the ACT college entrance examination in followed a Normal distribution with mean and standard deviation
(a) What is the probability that a single student randomly chosen from all those taking the test scores or higher? Show your work.
(b) Now take an SRS of students Who took the fest. What is the probability that the mean score of these students is or higher? Show your work
What does the CLT say? Asked what the central limit theorem says, a student replies, "As you take larger and larger samples from a population, the histogram of the sample values looks mote and more Normal." ls the student right? Explain your answer.
A newborn baby has extremely low birth weight (ELBW) if it weighs less than grams. A study of the health of such children in later years examined a random sample of children. Their mean weight at birth was grams. This sample mean is an unbiased estimator of the mean weight in the population of all ELBW babies, which means that
(a) in all possible samples of size from this population, the mean of the values of will equal .
(b) in all possible samples of size 219 from this population, the mean of the values of will equal .
(c) as we take larger and larger samples from this population, will get closer and closer to .
(d) in all possible samples of size from this population, the values of will have a distribution that is close to Normal.
(e) the person measuring the children's weights does so without any systematic error.
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