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Chapter 7: Q. 28 (page 457)
In a residential neighborhood, the median value of a house is . For which of the
following sample sizes is the sample median most likely to be above ?
(a)
(b)
(c)
(d)
(e) Impossible to determine without more information.
The correct answer is (a)
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According to government data, of American children under the age of 6 live in households with incomes less than the official poverty level. A study of learning in
early childhood chooses an SRS of children from one state and finds that .
a. Find the probability that at least of the sample are from poverty-level householdshouseholds.
b. Based on your answer to part (a), is there convincing evidence that the percentage of children under the age of 6 living in households with incomes less than the official poverty level in this state is greater than the national value of ? Explain your reasoning.
A large company is interested in improving the efficiency of its customer service and decides to examine the length of the business phone calls made to clients by its sales staff. Here is a cumulative relative frequency graph from data collected over the past year. According to the graph, the shortest 80% of calls will take how long to complete?
a. Less than 10 minutes
b. At least 10 minutes
c. Exactly 10 minutes
d. At least 5.5 minutes
e. Less than 5.5 minutes
Section II: Free Response Show all your work. Indicate clearly the methods you use, because you will be graded on the correctness of your methods as well as on the accuracy and completeness of your results and explanations.
The amount that households pay service providers for access to the Internet varies quite a bit, but the mean monthly fee is 50\( and the standard deviation is 20\). The distribution is not Normal: many households pay a low rate as part of a bundle with phone or television service, but some pay much more for Internet only or for faster connections. 11 A sample survey asks an SRS of 50 households with Internet access how much they pay. Let be the mean amount paid.
a. Explain why you can't determine the probability that the amount a randomly selected household pays for access to the Internet exceeds 55 .\(
b. What are the mean and standard deviation of the sampling distribution of ?
c. What is the shape of the sampling distribution of ? Justify your answer.
d. Find the probability that the average fee paid by the sample of households exceeds 55 .\)
Songs on an iPod Refer to Exercise 53 . How many songs would you need to sample if you wanted the standard deviation of the sampling distribution of to be 10 seconds? Justify your answer.
In a certain large population of adults, the distribution of IQ scores is strongly left skewed with a mean of 122 and a standard deviation of 5. Suppose 200 adults are randomly selected from this population for a market research study. For SRSs of size 200, the distribution of sample mean IQ score is
a. left-skewed with mean 122 and standard deviation 0.35.
b. exactly Normal with mean 122 and standard deviation 5.
c. exactly Normal with mean 122 and standard deviation 0.35.
d. approximately Normal with mean 122 and standard deviation 5.
e. approximately Normal with mean 122 and standard deviation 0.35.
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