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Chapter 7: Q.45 (page 441)
Decreasing the sample size from to would multiply the standard deviation by
(a) .
(b) .
(c) .
(d) .
(e) none of these.
The correct answer is (b).
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Identify the population, the parameter, the sample, and the statistic in each setting.
Stop smoking! A random sample of people who signed a card saying they intended to quit smoking were contacted nine months later. It turned out that of the sampled individuals had not smoked over the past six months.
The magazine Sports Illustrated asked a random sample of Division I college athletes, 鈥淒o you believe performance-enhancing drugs are a problem in college sports?鈥� Suppose that of all Division I athletes think that these drugs are a problem. Let be the sample proportion who say that these drugs are a problem.
The sampling distribution of has mean
(a) .
(b) .
(c) .
(d) .
(e) none of these.
Thousands of travelers pass through the airport in Guadalajara, Mexico, each day. Before leaving the airport, each passenger must pass through the Customs inspection area. Customs agents want to be sure that passengers do not bring illegal items into the country. But they do not have time to search every traveler鈥檚 luggage. Instead, they require each person to press a button. Either a red or a green bulb lights up. If the red light shows, the passenger will be searched by Customs agents. A green light means 鈥済o ahead.鈥� Customs agents claim that the proportion of all travelers who will be stopped (red light) is, because the light has probability of showing red on any push of the button. To test this claim, a concerned citizen watches a random sample of travelers push the button. Only get a red light.
(a) Assume that the Customs agents鈥� claim is true. Find the probability that the proportion of travelers who get a red light is as small as or smaller than the result in this sample. Show your work.
(b) Based on your results in (a), do you believe the Customs agents鈥� claim? Explain.
Dem bones (2.2) Osteoporosis is a condition in which the bones become brittle due to loss of minerals. To diagnose osteoporosis, an elaborate apparatus measures bone mineral density (BMD). BMD is usually reported in standardized form. The standardization is based on a population of healthy young adults. The World Health Organization (WHO) criterion for osteoporosis is a BMD score that is standard deviations below the mean for young adults. BMD measurements in a population of people similar in age and gender roughly follow a Normal distribution.
(a) What percent of healthy young adults have osteoporosis by the WHO criterion?
(b) Women aged to are, of course, not young adults. The mean BMD in this age group is about 2 on the standard scale for young adults. Suppose that the standard deviation is the same as for young adults. What percent of this older population has osteoporosis?
The gypsy moth is a serious threat to oak and aspen trees. A state agriculture department places traps throughout the state to detect the moths. When traps are checked periodically, the mean number of moths trapped is only but some traps have several moths. The distribution of moth counts is discrete and strongly skewed, with standard deviation.
(a) What are the mean and standard deviation of the average number of moths intraps?
(b) Use the central limit theorem to help you find the probability that the average number of moths in traps is greater than.
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