Question 1

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.

Accepted Answer

$\hat{p}=247 / 650=0.380
$
The $ 95 \% $ confidence interval for $ \mathrm{p} $ is $ 0.380 \pm 2 \sqrt{\frac{0.38(0.62)}{650}}=0.380 \pm 0.038 $ or $ 0.342 $ to $ 0.418 $

Question 2

In a poll of 200 voters, 55% said that they supported a local ban on smoking in restaurants. The margin of error was reported as 5%. Which one of the following statements reflects the accuracy of this result?

Accepted Answer

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. C

Question 3

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.

Accepted Answer

204

Question 4

A government survey conducted to estimate the mean price of houses in a metropolitan area is designed to have a margin of error of $10,000. Pilot studies suggest that the population standard deviation is $80,000. Estimate the minimum sample size needed to estimate the population mean with the stated accuracy.

Accepted Answer

The answer of A government survey conducted to estimate the...

Question 5

12% of the residents of one town are aged over 70. The distribution of sample proportions of samples of 210 residents is normal with a mean of 0.12 and a standard deviation of 0.022.
Suppose that you select a sample of 210 residents and find that the proportion aged over 70 in the sample is 0.09. What is the z-score corresponding to this sample proportion?

Accepted Answer

The answer of 12% of the residents of one town...

Question 6

A sample of nine students is selected from among the students taking a particular exam. The nine students were asked how much time they had spent studying for the exam and the responses (in hours) were as follows:
18, 7, 10, 13, 12, 16, 5, 20, 21
Estimate the mean study time of all students taking the exam. Round your answer to the nearest tenth of an hour if necessary.

Accepted Answer

A)   13 hours
B)   12.2 hours
C)   13.6 hours
D)   It is not possible to estimate the population mean from this sample data

Question 7

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, 1, 7, 10, and 8 pounds.
Estimate the population mean weight to the nearest tenth of a pound.

Accepted Answer

The answer of An internet sales company decided to charge...

Question 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.

Accepted Answer

The answer of A sample of 144 college freshmen had...

Question 9

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 costs is assumed to be $50, what is the minimum sample size he should use?

Accepted Answer

The answer of A researcher wants to estimate the mean...

Question 10

A researcher wishes to estimate the proportion of college students who cheat on exams. A poll of 490 college students showed that 33% of them had, or intended to, cheat on examinations.
Find the margin of error for the 95% confidence interval.

Accepted Answer

The answer of A researcher wishes to estimate the proportion...

Question 11

There are 318 teachers at a college. Among a sample of 115 teachers from this college, 67 have doctorates. Based on this sample, estimate the population proportion of teachers at this college with doctorates.

Accepted Answer

A)   0.42
B)   185
C)   0.61
D)   0.58

Question 12

A random sample of 30 households was selected from a particular neighborhood. The number of cars for each household is shown below. Estimate the mean number of cars per household for the population of households in this neighborhood. Give the 95% confidence interval. 
$$\begin{array} { l l l l l l l l l l } 
2 & 0 & 1 & 2 & 3 & 2 & 1 & 0 & 1 & 4 \
1 & 3 & 2 & 0 & 1 & 1 & 2 & 3 & 1 & 2 \
1 & 0 & 2 & 3 & 0 & 2 & 2 & 1 & 0 & 2
\end{array}$$

Accepted Answer

The answer of A random sample of 30 households was...

Question 13

A medical researcher wishes to estimate the mean systolic blood pressure of heart surgery patients the day following surgery. She desires a margin of error of 1.6 mmHg. Past studies suggest that a population standard deviation of 43 mmHg is reasonable. Estimate the minimum sample size needed to estimate the population mean with the stated accuracy.

Accepted Answer

The answer of A medical researcher wishes to estimate the...

Question 14

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 
$\begin{array}{l}
\begin{array}{lllllllllllllll}
1 & 2 & 3 & 3 & 6 & 6 & 6 & 7 & 7 & 7 & 7 & 8 & 11 & 11 & 12\

13&13&14&14&14&15&16&17&18&19&19&21&22&23&25 \
\end{array} \
\end{array}$ 
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..

Accepted Answer

The answer of During a year when there was a...

Question 15

Eleven female college students are selected at random and asked their heights. The heights (in inches) are as follows:
67, 59, 64, 69, 65, 65, 66, 64, 62, 64, 62
Estimate the mean height of all female students at this college. Round your answer to the nearest tenth of an inch if necessary.

Accepted Answer

A)   It is not possible to estimate the population mean from this sample data
B)   64.3 inches
C)   64.9 inches
D)   63.7 inches

Question 16

In a poll of 615 voters in a certain city, 51% 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?

Accepted Answer

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 much 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

Question 17

There are 349 teachers at a college. Among a sample of 110 teachers from this college, 66 have doctorates. Based on this sample, estimate the number of teachers at this college without doctorates.

Accepted Answer

The answer of There are 349 teachers at a college....

Question 18

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?". 642 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 14,642 who would respond "No" to the question.

Accepted Answer

The answer of In a national poll, 1036 people were...

Question 19

In one city, there are 2640 5-year-old children of whom 977 live with one parent only. Among a sample of 500 of the 5-year-old children from this city, 170 live with one parent only. Find the sample proportion of 5-year-old children who live with only one parent.

Accepted Answer

A)   0.37
B)   0.34
C)   0.4
D)   185

Question 20

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?

Accepted Answer

The answer of Stanford-Binet IQ scores have a population mean...

Exam 8: From Samples to Populations