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Chapter 8: Q.3 (page 481)
Going to the prom Tonya wants to estimate what proportion of the seniors in her school plan to attend the prom. She interviews an SRS of of the seniors in her school and finds that plan to go to the prom
The sample proportion is.
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Watching TV (6.1, 7.3) Choose a young person (aged to ) at random and ask, 鈥淚n the past seven days, how many days did you watch television?鈥� Call the response for short. Here is the probability distribution for .
(a) What is the probability that ? Justify your answer.
(b) Calculate the mean of the random variable X. Interpret this value in context.
(c) Suppose that you asked randomly sele
cted young people (aged to ) to respond to the question and found that the mean of their responses was . Would this result surprise you? Justify your answer.
Trace metals found in wells affect the taste of drinking water, and high concentrations can pose a health risk. Researchers measured the concentration of zinc (in milligrams/liter) near the top and the bottom of randomly selected wells in a large region. The data are provided in the table below.
(a) Construct and interpret a confidence interval for the mean difference in the zinc concentrations from these two locations in the wells.
(b) Does your interval in part (a) give convincing evidence of a difference in zinc concentrations at the top and bottom of wells in the region? Justify your answer.
63. Give it some gas! Computers in some vehicles calculate various quantities related to performance. One of these is fuel efficiency, or gas mileage, usually expressed as miles per gallon (mpg). For one vehicle
equipped in this way, the miles per gallon were recorded each time the gas tank was filled and the computer was then reset. Here are the mpg values for a random sample of of these records:
Construct and interpret a confidence interval for the mean fuel efficiency M for this vehicle.
A researcher plans to use a random sample of families to estimate the mean monthly family income for a large population. Aconfidence interval based on the sample would be ______ than a 90% confidence interval.
(a) narrower and would involve a larger risk of being incorrect
(b) wider and would involve a smaller risk of being incorrect
(c) narrower and would involve a smaller risk of being incorrect
(d) wider and would involve a larger risk of being incorrect
(e) wider, but it cannot be determined whether the risk of being incorrect would be larger or smaller
Explain briefly why each of the three conditions鈥擱andom, Normal, and Independent鈥攊s important when constructing a confidence interval.
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