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Chapter 7: Q.57 (page 455)
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.
The student is not right
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You work for an advertising agency that is preparing a new television commercial to appeal to women. You have been asked to design an experiment to compare the effectiveness of three versions of the commercial. Each subject will be shown one of the three versions and then asked about her attitude toward the product. You think there may be large differences between women who are employed and those who are not. Because of these differences, you should use
(a) a block design, but not a matched pairs design
(b) a completely randomized design.
(c) a matched pairs design.
(d) a simple random sample.
(e) a stratified random sample.
Unlisted numbers: A telemarketing firm in Los Angeles uses a device that dials residential telephone numbers in that city at random. Of the first numbers dialed, are unlisted. This is not surprising because of all Los Angeles residential phones are unlisted.
The California Department of Fish and Game publishes a list of the state鈥檚 endangered animals. The reptiles on the list are given across the bottom of the question.
(a) Describe how you would use Table D at line 111 to choose an SRS of 3 of these reptiles to study.
(b) Use your method from part (a) to select your sample. Identify the reptiles you chose.
Desert tortoise Green sea turtle Loggerhead sea turtle Giant garter snake Olive Ridley sea turtle Leatherback sea turtle Barefoot banded gecko San Francisco garter snake Island night lizard Alameda whip snake Coachella Valley fringe-toed lizard Flat-tailed horned lizard Southern rubber boa blunt-nosed leopard lizard
The student newspaper at a large university asks an SRS of undergraduates, 鈥淒o you favor eliminating the carnival from the term-end celebration?鈥� All in all, of the are in favor. Suppose that (unknown to you) of all undergraduates favor eliminating the carnival. If you took a very large number of SRSs of size from this population, the sampling distribution of the sample proportion would be
(a) exactly Normal with mean and standard deviation of
(b) approximately Normal with mean and standard deviation .
(c) exactly Normal with mean and standard deviation .
(d) approximately Normal with mean and standard deviation .
(e) heavily skewed with mean and standard deviation .
Do you go to church? What sample size would be required to reduce the standard deviation of the sampling distribution to one-third the value you found in Exercise 36 (b)? Justify your answer.
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