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Spring 2008 Math 227
Test #3 (ch 7, 8 & 9)
Name: ____________________
Show all necessary work for full credit. Total: 100 points.
1.
(10 points)
Suppose that the weight of the cereal in boxes of Loopy Froots breakfast cereal is normally
distributed. A consumer advocate group randomly sampled 8 boxes of Loopy Froots and weighed
the contents (in grams): 535, 540, 565, 575, 535, 558, 564, and 550.
a. Find the sample mean and sample standard deviation.
b. Construct a 95% confidence interval for the mean average of the weight of the cereal in boxes of
Loop Froots.
2.
(10 points)A marketing research is conducting a survey to determine what proportion of consumers
between the ages of 18 and 35 own an iPod. Sixty individuals in that age range were randomly
sampled and 11 of them own iPod.
a. Find a point estimate for the proportion of consumers who own iPod.
b. Construct a 90% confidence interval for p
3.
(10 points)Assume that the previous Test scores were normally distributed. For a random sample of size
5, the scores were 72, 48, 65, 59 and 37.
a. Find the sample mean, and the sample standard deviation
b. Construct the 95%-confidence interval for standard deviation of the previous Test scores.
4.
(10 points)A
market researcher for a consumer electronics company wants to study the weekly TV
viewing habits of residents of a particular city. A random sample of 41 respondents is selected and
the sample resulted a mean of 15.3 hours with 3.8 hours standard deviation. Assume that the amount
of time of TV viewing per week is normally distributed. Test the claim at 5% significant level that
the mean of viewing habit is more than 14 hours per week.
5.
(8 points)The
Wechsler IQ test is designed so that the mean is 100 and the standard deviation is 15 for
the population of normal adults. Find the sample size necessary to estimate the mean IQ score of
statistics students. We want to be 95% confident that our sample mean is within 2 IQ points of the
true mean. Assume   15 .
6.
(12 points)
Eight different families are tested for the number of gallons of water a day they use before
and after viewing a conservation video. At the 0.01 significance level, test the claim that the mean is
the same before and after the viewing. Assume the sample is drawn from normal population.
Before
34
33
38
33
40
31
33
35
After
33
28
25
35
31
28
35
28
7.
(10 points)A
section of Highway 405 in Los Angeles has a speed limit of 65 mi/h, and recorded speeds
are listed below for randomly selected cars traveling on northbound and southbound lanes.
Highway 405 North:
68
68
72
73
65
74
73
72
68
65
65
73
66
71
68
74
66
71
65
73
Highway 405 South:
59
75
70
56
66
75
68
75
62
72
60
73
61
75
58
74
60
73
58
75
Assume that the speeds are from normally distributed population; test the claim that the mean speed
on the northbound lanes is equal to the mean speed on the southbound lanes. Use   0.01
8.
(10 points)In
a study of store checkout scanners, 1234 items were checked and 20 checked items were
found to be overcharges, and 1214 checked items were not overcharges. Use a 0.05 significance
level to test the claim that with scanners, 1% of sales are overcharges.
9.
(10 points)A
survey of 436 workers showed that 192 of them said that it was seriously unethical to
monitor employee e-mail. When 121 senior-level bosses were surveyed, 40 said that it was seriously
unethical to monitor employee e-mail. Construct a 90% confidence interval estimate of the
difference between the two population proportions. Is there a substantial gap between the employees
and bosses?
10. (10 points)Use a 0.05 significance level to test the claim that heights of female supermodels vary less
than the heights of women in general. The standard deviation of heights of the population of women
is 2.5 in. Listed below are the heights (in inches) of randomly selected supermodels. Assume that
the heights are from normally distributed population.
71
71
70
69
69.5 70.5 71
72
70
70
69
69.5 69
70
70
66.5 70
71