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Chapter 7: Q.46 (page 441)
The sampling distribution of is approximately Normal because
(a) there are at least Division I college athletes.
(b) and .
(c) a random sample was chosen.
(d) a large sample size like guarantees it.
(e) the sampling distribution of always has this shape.
The correct answer is (b)and.
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Stop the carl A car company has found that the lifetime of its disc brake pads varies from car to car according to a Normal distrilustion with mean miles and standard deviationmiles. The company installs a new brand of brake pads on an SRS of cars.
(a) If the new brand has the same lifetime distribution as the previous bye of brake pad, what is the sampling distribution of the mean lifetime ?
(b) The average life of the pads an these cars turns out to be miles. Find the probability that the sample mean lifetime is miles or less if the lifetime distribution is unchanged, What conclusion would you draw?
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
Your mail-order company advertises that it ships of its orders within three working days. You select an SRS of of the orders received in the past week for an audit. The audit reveals that of these orders were shipped on time.
(a) If the company really ships of its orders on time, what is the probability that the proportion in an SRS of orders is as small as the proportion in your sample or smaller? Follow the four-step process.
(b) A critic says, 鈥淎ha! You claim , but in your sample, the on-time percentage is lower than that. So the claim is wrong.鈥� Explain in simple language why your probability calculation in (a) shows that the result of the sample does not refute the claim.
Scrabble In the game of Scrabble, each player begins by drawing 7 tiles from a bag containing 100 tiles. There are 42 vowels, 56 consonants, and 2 blank tiles in the bag. Cait chooses an SRS of 7 tiles. Let be the proportion of vowels in her sample.
(a) Is the condition met in this case? Justify your answer.
(b) Is the Normal condition met in this case? Justify your answer.
The number of undergraduates at Johns Hopkins University is approximately , while the number at Ohio State University is approximately . At both schools, a simple random sample of about of the undergraduates is taken. Each sample is used to estimate the proportion p of all students at that university who own an iPod. Suppose that, in fact, at both schools. Which of the following is the best conclusion?
(a) The estimate from Johns Hopkins has less sampling variability than that from Ohio State.
(b) The estimate from Johns Hopkins has more sampling variability than that from Ohio State.
(c) The two estimates have about the same amount of sampling variability.
(d) It is impossible to make any statement about the sampling variability of the two estimates since the students surveyed were different.
(e) None of the above
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