Download Practice Test 3 answers

Test 3 Venable Statistics Fall 2011
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Please show all work - even work done by calculator. Be sure to show all steps of hypothesis tests
and p-value tests.
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1. According to a survey by the National Retail Association, the average amount that
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households in the United States platmed to spend on gifts, decorations, greeting cards, and _ '&
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food during the 2009 holiday season was $940. Suppose that a recent randon: sample?f ~! ~:o
324 households showed that they plan to spend an average of $1 005 on such Items dunng
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this year's holiday season with a standard deviation of$330. Test at the 1% significance 1:)(.:= , 0 r
level whether the mean of such planned holiday-related expenditures for households for this
year differs from $940 .
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~'1-' 2. In 2000, 19 million registered voters failed to vote in the presidential election. The most frequently given reason for not voting was "too busy," cited by 20.9% of the respondents. y\::' L SO
Suppose that a random sample of250 registered voters who did not vote in the November ~ .... . C"6 \ . 2002 midterm elections showed that 18.1 % of them stated the main reason for not voting r
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too busy was less than 20.9%?
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3. According to Money magazine, the average net worth ofD.S. households in 2008 was
$355,000. Assume that this mean is based on a random sample of 500 households and that
the sample standard deviation is $125,000. Construct a 99% confidence interval for the
2008 mean net worth of all U.S. households.
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4. According to a survey, mothers with children under age 18 spent an average of 16.87 hours
per week online. Suppose that this mean is based on a random sample of 1000 such
mothers and that the population standard deviation is 3.2 hours per week. Construct a 95%
confidence interval for the corresponding population mean for all such mothers .
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5. A marketing researcher wants to find a 95% confidence interval for the mean amount that
visitors to a theme park spend per person per day. She knows that the standard deviation of
the amounts spent per person per day by all visitors to this park is $11 . How large a sample
should the researcher select so that the estimate will be within $2 of the population mean?
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6. A consumer agency wants to estimate the proportion of all drivers who wear seat belts
while driving. Assume that a preliminary study has shown that 76% of drivers wear seat
belts while driving. How large should the sample size be so that the 99% confidence
interval for the population proportion has a maximum error ofO.03? E -;.. 03
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7. A sample of 73 female workers and another sample of 47 male workers from a state
produced mean weekly earnings of $729.51 for the females and $765.40 for the males.
Suppose that the population standard deviations of the weekly earnings are $80.00 for the
females and $96 .51 for the males. Test at the 1% significance level if the mean weekly
~ earnings for all male workers in this state is higher than the mean weekly earnings for all
~ female workers.
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8. A consumer advocacy group suspects that a local supermarket's 10-ounce packages of
cheddar cheese actually weigh less than 10 ounces. The group took a random sample of 36
such packages and found that the mean weight for the sample was 9.955 ounces. The
population standard deviation is known to be 0.15 ounces. Use the p-value approach to test
the hypothesis that the mean weight of all such packages is less than 10 ounces.
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9. The manager of a bank claims that the mean waiting time for all customers at that bank is
not more than 10 minutes. A sample of 35 customers who visited this bank gave a mean
waiting time of 12 minutes and a standard deviation of3.4 minutes. Use the critical value
approach to test at the 2.5% significance level if the mean waiting time for all customers
who visit this bank is greater than 1b minutes. Assume that the waiting time for all
customers is normally distributed .
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10. A random sample of 9 students was selected to test for the effectiveness of a special course
designed to improve memory. The following talbe gives the scores in a memory test given
to these students before and after this course.
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