Statistical Reasoning for Everyday Life

Statistical Reasoning for Everyday Life Chapter 8 (From Samples to Populations)
1)
An internet sales company decided to. charge the same amount for shipping and handling on all
packages. To determine the amount, they took a random sample of previous sales to determine the
average weight. The packages weighed 4, 17, 12,9, 13 and 8 pounds. Estimate the population
mean weight to the nearest tenth of a pound.
2)
Stanford-Binet IQ scores have a population mean of 100 and a standard deviation of 16. A
community college selects 64 students at random to test and finds that the sample mean is 105.6.
What is the z-score associated with this sample mean?
3)
A random sample of 100 college students had an average student loan of $816. This was 1.3
standard deviations above the mean of the sampling distribution of the sample mean. If another
random sample of 100 students were taken, what is the probability that that sample would have a
mean greater than $8l6?
4)
In a random sample of 400 jelly beans, there were 88 red ones, What is the sample proportion of
red jelly beans?
5)
In a national poll, 1036 people were interviewed and asked the question, "Do you think it should
be legal to carry a concealed weapon if it is properly registered?". 542 people responded "No." If
the city of Upton is typical of the entire U.S., estimate the number of people in this city with a
population of 13,746 who would respond "No" to the question.
6)
Half of all people with social security numbers (SSNs) have a number that ends with a 0, 2,4, 6,
or 8. A sample of 100 students found that 45 had even numbered SSNs. The sample proportion
has a z-score of -1.0. If a second =sampJe of 100 students is taken, what is the probability that the
sample proportion has a z-score less than -1.0?
7)
Jf a sample of size 900 has a mean of 452 and a standard deviation of 96, what is the margin of
error for a 95% confidence interval?
8)
A sample of 144 college freshmen had a mean mathematics placement test score of 17.82 with a
standard deviation of 4.8. Find a 95% CI for the population mean placement score for all
freshmen.
9)
A researcher wants to estimate the starting salary of Assistant Professors in Economics with a
margin of error of $400 for a 95% confidence interval. If the standard deviation of those salaries
is assumed to be $3200, what is the minimum sample size she should use?
10) A researcher wants to estimate the mean cost of textbooks per year for students at a large
university. He wants a margin of error of $10 for a 95% confidence interval. If the standard
deviation of those cost is assumed to be $50, what is the minimum sample size he should use?
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11) During a year when there was a bad flu epidemic, a school district sampled 30 student records to
get an estimate of the mean number of absences of all of the students. The absences recorded
were
1 2 3 3 6 6 6 7 7 7 7 8111112
13 13 14 14 14 15 16 17 18 19 1921222325
The sample mean is 12.0 absences and the standard deviation is 6.6384. Find a 95% confidence
interval for the population mean to two decimal places ..
12) In a poll of 400 U.S. adults, 84 indicated that they did not know how to swim. Find the margin of
error .E for estimating the proportion of all U.S. adult s who cannot swim with a 95% confidence
interval.
13) A survey of 650 adult males found that 247 of them held current fishing licenses. Find a- 95%
confidence interval (to three decimal places) for the proportion of all adult males who hold current
fishing licenses.
14) A campaign committee expects the next election for mayor to be close. The members want to take
a poll to see how their candidate is likely to fare. What is the minimum sample size needed to
estimate their candidate's percentage of the vote to within 4%?
15) In a poll of 200 voters, 55% said that they supported a local ban on smoking ill restaurants. The
margin oferror was reported as 5%. Which one of the following statements reflects the accuracy
of this result?
A) The reported margin of error is consistent with the sample size.
B) There is not enough information to determine whether the margin of error is consistent
with the sample size.
C) The sample size is too small to achieve the stated margin of error.
D) For the given sample size, the margin of error .should be smaller than stated.
I & A random sample of 30 long distance runners aged 20-25 was selected from a running club. The
resting heart rates (in beats per minute) of the runners are shown below. Estimate the mean resting
heart rate for the population of long distance runners aged 20-25. Give the 95% confidence
interval to one decimal place. The sample mean is 68 and the sample standard deviation is 8.133.
62
70
61
64
75
54
72
68
74
54
75
70
62
66
79
73
81
60
66
76
67
62
62
73
70
86
76
60
53
69
11; A poll of 1500 voters in one district showed that 64% of them would favor stricter gun control
laws. Find the margin of error for the 95% confidence interval for this study.
18.) A medical researcher ";"IS~s to estim.rt~ what prop~rti~n ~f babies born at a particular hospital are --born by Caesarean section. In a random sample of 100 births at the hospital, 34% were Caesarean
sections. Find the 95% confidence interval for the population proportion. Show 4 decimal places.
1q) A population proportion is to be estimated. Estimate the minimum sample size needed to achieve a
margin of error of 7 percentage points with a 95% degree of confidence.
),b) In a poll of 615 voters in a certain city, 68% said that they backed a bill that would limit growth
and development in their city. The margin of error in the poll was reported as 4 percentage points
(with a 95% degree of confidence). Which statement is correct?
A) The sample size is too small to achieve the stated margin of error
B) The stated margin of error could be achieved with a smaller sample size
C)
There is not enough information to determine whether the margin of error is consistent
with the sample size
D) The reported margin of error is consistent with the sample size
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