Deck 8: From Samples to Populations

Question 1

Among a random sample of 500 college students, the mean number of hours worked per week at non-college related jobs is 14.6. This mean lies 0.4 standard deviations below the mean of the sampling distribution. If a second sample of 500 students is selected, what is the probability that for the second sample, the mean number of hours worked will be less than 14.6?

A) 0.5
B) 0.6179
C) 0.6554
D) 0.3446

Answer 1

0.3446

Question 2

A population proportion is to be estimated. Estimate the minimum sample size needed to achieve a margin of error E = 0.01with a 95% degree of confidence.

Answer 2

10,000

Question 3

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 $70,000. Estimate the minimum sample size needed to estimate the population mean with the stated accuracy.

Answer 3

196

Question 4

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.

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 5

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.

Question 6

A researcher wishes to estimate the mean amount of money spent per month on food by households in a certain neighborhood. She desires a margin of error of $30. Past studies suggest that a population standard deviation of $248 is reasonable. Estimate the minimum sample size needed to estimate the population mean with the stated accuracy.

Question 7

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.

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

Question 8

Of the 6796 students in one school district, 1537 cannot read up to grade level. Among a sample of 812 of the students from this school district, 211 cannot read up to grade level. Find the sample proportion of students who cannot read up to grade level.

A) 0.14
B) 0.26
C) 211
D) 0.23

Question 9

Among a random sample of 150 employees of a particular company, the mean commute distance is 29.6 miles. This mean lies 1.2 standard deviations above the mean of the sampling distribution. If a second sample of 150 employees is selected, what is the probability that for the second sample, the mean commute distance will be less than 29.6 miles?

A) 0.8849
B) 0.5
C) 0.1131
D) 0.1151

Question 10

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.
$$\begin{array} { l l l l l l l l l l } 2 & 0 & 1 & 2 & 3 & 2 & 1 & 0 & 1 & 4 \\1 & 3 & 2 & 0 & 1 & 1 & 2 & 3 & 1 & 2 \\1 & 0 & 2 & 3 & 0 & 2 & 2 & 1 & 0 & 2\end{array}$$

Question 11

Monthly incomes of employees at a particular company have a mean of $ 5954. The distribution of sample means for samples of size 70 is normal with a mean of $ 5954 and a standard deviation of $259. Suppose you take a sample of size 70 employees from the company and find that their mean monthly income is $ 5747. How many standard deviations is the sample mean from the mean of the sampling distribution?

A) 0.8 standard deviations above the mean
B) 0.8 standard deviations below the mean
C) 7.3 standard deviations below the mean
D) 207 standard deviations below the mean

Question 12

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.

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 13

In a poll of 400 voters in a certain state, 61% said that they opposed a voter ID bill that might hinder some legitimate voters from voting. 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 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.

Question 14

30% of the fifth grade students in a large school district read below grade level. The distribution of sample proportions of samples of 100 students from this population is normal with a mean of 0.30 and a standard deviation of 0.045. Suppose that you select a sample of 100 fifth grade students from this district and find that the proportion that reads below grade level in the sample is 0.36. What is the probability that a second sample would be selected
with a proportion less than 0.36?

Question 15

A researcher wishes to estimate the proportion of college students who cheat on exams. A poll of 560 college students showed that 27% of them had, or intended to, cheat on examinations.
Find the 95% confidence interval.

Question 16

A sample of 64 statistics students at a small college had a mean mathematics ACT score of 28 with a standard deviation of 4. Estimate the mean mathematics ACT score for all statistics students at this college. Give the 95% confidence interval.

Question 17

Scores on a particular test have a mean of 64.6 and a standard deviation of 15.0. Suppose you take a sample of size 100 of test scores and find that the mean is 63.1. What is the z-score corresponding to this sample mean?

A) 1.5
B) ?1.5
C) ?0.1
D) ?1.0

Question 18

In one city, there are 1780 5-year old children of whom 556 live with one parent only. Among a sample of 615 of the 5-year old children from this city, 226 live with one parent only. Find the population proportion of 5-year olds who live with only one parent.

A) 0.35
B) 556
C) 0.37
D) 0.31

Question 19

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.

Question 20

Sample size = 400, sample mean = 44, sample standard deviation = 16. What is the margin of error?

Question 21

Nine employees of a company are selected at random and asked how far they commute to work each day. The distances (in miles) are as follows:
32, 18, 44, 29, 25, 38, 5, 48, 12
Estimate the mean commute distance of all employees of the company. Round your answer to the nearest tenth of a mile if necessary.

A) It is not possible to estimate the population mean from this sample data
B) 26.7 miles
C) 27.9 miles
D) 29 miles

Question 22

At one hospital, a random sample of 100 women giving birth to their first child is selected. among this sample, the mean age was 26.3 with a standard deviation of 4.9. Estimate the mean age of all women giving birth to their first child at this hospital. Give the 95% confidence interval to two decimal places.

Question 23

Among a sample of 78 students selected at random from one college, the mean number of siblings is 1.5 with a standard deviation of 1.2. Estimate the mean number of siblings for all students at this college. Give the 95% confidence interval to two decimal places.

Question 24

A medical researcher wishes to estimate what proportion of 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.

Question 25

Sample size = 1225, sample mean = 214, sample standard deviation = 49. What is the margin of error?

Question 26

The ages of employees at a particular company have a mean of 39. The distribution of sample means for samples of size 200 is normal with a mean of 39 and a standard deviation of 0.79.
Suppose you take a sample of size 200 employees from the company and find that their mean age is 41.3. How many standard deviations is the sample mean from the mean of the sampling distribution?

A) 2.3 standard deviations above the mean
B) 2.9 standard deviations above the mean
C) 41.2 standard deviations above the mean
D) 3.2 standard deviations above the mean

Question 27

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?

Question 28

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.

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

Question 29

A poll of 1000 voters in one district showed that 57% of them would favor stricter gun control laws. Find the margin of error for the 95% confidence interval for this study.

Question 30

Among a random sample of 150 employees of a particular company, the mean commute distance is 28.1 miles. This mean lies 0.7 standard deviations below the mean of the sampling distribution. If a second sample of 150 employees is selected, what is the probability that for the second sample, the mean commute distance will be at least 28.1 miles?

A) 0.7580
B) 0.5000
C) 0.2420
D) 0.2743

Question 31

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.

Question 32

Question 33

A college teacher wishes to estimate the mean number of hours worked per week at non college related jobs by full time students at the college. He desires a margin of error of 0.6 hours. Past studies suggest that a population standard deviation of 14.3 hours is reasonable.

Question 34

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.

Question 35

12% of the residents of one town are aged over 70. The distribution of sample proportions for samples of 140 residents is normal with a mean of 0.12 and a standard deviation of 0.027.
Suppose that you select a sample of 140 residents and find that the proportion aged over 70 in the sample is 0.08. What is the probability that a second sample would be selected with a proportion greater than 0.08?

Question 36

A government survey conducted to estimate the mean price of houses in a metropolitan area is designed to have a margin of error of $6000. Pilot studies suggest that the population standard deviation is $49,000. Estimate the minimum sample size needed to estimate the population mean with the stated accuracy.

Question 37

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.

Question 38

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?

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 39

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. $$\begin{array} { l l l l l l l l l l } 62 & 70 & 61 & 64 & 75 & 54 & 72 & 68 & 74 & 54 \\75 & 70 & 62 & 66 & 79 & 73 & 81 & 60 & 66 & 76 \\67 & 62 & 62 & 73 & 70 & 86 & 76 & 60 & 53 & 69\end{array}$$

Question 40

There are 13,339 eligible voters in one town. Among a sample of 828 eligible voters from this town, 396 say that they plan to vote in the next mayoral election. Based on this sample, Estimate the number of eligible voters in this town who will not vote in the next mayoral election.

A) 6959
B) 432
C) 6380
D) 0.52

Question 41

The college daily reported: ?600 students living in university housing were polled. 360 said that they were satisfied with their living conditions. Based on this survey we conclude that 60% of students living in dormitories are satisfied. The margin of error of the study is 4 percentage points (with a 95% degree of confidence). Which statement is correct?

A) There is not enough information to determine whether the margin of error is consistent with the sample size.
B) The stated margin of error could have been achieved with a smaller sample size.
C) A larger sample should be used to achieve the stated margin of error.
D) The margin of error is consistent with the sample size.
104

Question 42

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?

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.

Question 43

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.

Question 44

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.

Question 45

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 =sample of 100 students is taken, what is the probability that the sample proportion has a z-score less than -1.0?

Question 46

A population proportion is to be estimated. Estimate the minimum sample size needed to achieve a margin of error of E = 0.056 with a 95% degree of confidence.

Question 47

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 5%?

Question 48

In a random sample of 400 jelly beans, there were 88 red ones. What is the sample proportion of red jelly beans?

Question 49

The weight (in pounds) of a random sample of 32 new born babies, born at a particular hospital are given below. Estimate the mean weight of the population of new born babies born at this hospital. Give the 95% confidence interval to two decimal places. The sample mean is 7.19 pounds and the standard deviation is 0.844 pounds. $$\begin{array} { l l l l l l l l } 8.0 & 6.2 & 6.8 & 7.1 & 6.8 & 8.6 & 7.4 & 6.4 \\7.4 & 7.0 & 6.0 & 7.8 & 9.0 & 7.3 & 6.5 & 5.8 \\8.4 & 7.6 & 7.2 & 6.5 & 8.5 & 7.1 & 6.3 & 6.9 \\7.0 & 5.9 & 8.3 & 6.6 & 7.3 & 7.7 & 6.4 & 8.2\end{array}$$

Question 50

A researcher wishes to estimate the proportion of left-handers among a certain population. In a random sample of 900 people from the population, 74% are left-handed. Find the margin of error for the 95% confidence interval.

Question 51

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 $3600, what is the minimum sample size she should use?

Question 52

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 $816?

Question 53

If 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?

Question 54

A researcher wishes to estimate the proportion of left-handers among a certain population. In a random sample of 690 people from the population, 16.4% are left-handed. Find the 95% confidence interval for the population proportion of left-handers to four decimal places.

Question 55

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.

Question 56

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. adults who cannot swim with a 95% confidence interval.

Question 57

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..

Question 58

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?

Question 59

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.

Question 60

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?