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Chapter 8: Q 77. (page 543)
Estimating BMI The body mass index (BMI) of all American young
women is believed to follow a Normal distribution with a standard deviation of about . How large a sample would be needed to estimate the mean BMI 渭 in this population to within with confidence?
Sample size is.
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A school of fish Refer to Exercise 74.
a. Explain why it was necessary to inspect a graph of the sample data when checking the Normal/Large Sample condition.
b. According to the packaging, there are supposed to be goldfish in each bag of crackers. Based on the interval, is there convincing evidence that the average number of goldfish is less than ? Explain your answer.
Can you taste PTC? PTC is a substance that has a strong bitter taste for some people and is tasteless for others. The ability to taste PTC is inherited. About of Italians can taste PTC, for example. You want to estimate the proportion of Americans who have at least one Italian grandparent and who can taste PTC.
a. How large a sample must you test to estimate the proportion of PTC tasters within with confidence? Answer this question using the estimate as the guessed value for .
b. Answer the question in part (a) again, but this time use the conservative guess. By how much do the two sample sizes differ?
After deciding on a confidence level, the researcher is deciding between a sample of size and a sample of size . Compared with using a sample size of , a confidence interval based on a sample size of will be
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. narrower and would have the same risk of being incorrect.
One reason for using a t distribution instead of the standard Normal distribution to find critical values when calculating a level C confidence interval for a population mean is that
a. can be used only for large samples.
b. requires that you know the population standard deviation .
c. requires that you can regard your data as an SRS from the population.
d. requires that the sample size is less than of the population size.
e. a critical value will lead to a wider interval than a critical value.
A Gallup poll found that only of American adults expect to inherit money or valuable possessions from a relative. The poll鈥檚 margin of error was 卤3 percentage points at a confidence level. This means that
a. the poll used a method that gets an answer within 3% of the truth about the population of the time.
b. the percent of all adults who expect an inheritance must be between and .
c. if Gallup takes another poll on this issue, the results of the second poll will lie between and .
d. there鈥檚 a 95% chance that the percent of all adults who expect an inheritance is between
25% and 31%.
e. Gallup can be 95% confident that between 25% and 31% of the sample expect an inheritance.
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