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?

Accepted Answer

The mean of the first sample is 0.4 standard deviations below the mean of the sampling distribution, which corresponds to a z-score of -0.4. The probability of a z-score being less than -0.4 is 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.

Accepted Answer

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.

Accepted Answer

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.

Accepted Answer

The sample mean is the best estimate of the population mean. The sample mean is 64.3 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.

Accepted Answer

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

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.

Accepted Answer

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

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.

Accepted Answer

The answer of There are 318 teachers at a college....

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.

Accepted Answer

The sample proportion is calculated by dividing the number of students in the sample who cannot read up to grade level (211) by the total number of students in the sample (812). So, 211/812 = 0.26.

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?

Accepted Answer

The mean of the first sample is 1.2 standard deviations above the mean of the sampling distribution. Therefore, the probability that the second sample mean is less than 29.6 miles is the probability of being below 1.2 standard deviations above the mean, which is approximately 0.8849.

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

Accepted Answer

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

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?

Accepted Answer

The sample mean is $5747, which is $207 below the population mean of $5954. Dividing this difference by the standard deviation of the sampling distribution ($259) gives approximately 0.8 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.

Accepted Answer

The mean study time is calculated by summing all the study times and dividing by the number of students: (18 + 7 + 10 + 13 + 12 + 16 + 5 + 20 + 21) / 9 = 13.6 hours.

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?

Accepted Answer

The answer of In a poll of 400 voters in...

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?

Accepted Answer

The answer of 30% of the fifth grade students in...

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.

Accepted Answer

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

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.

Accepted Answer

The answer of A sample of 64 statistics students at...

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?

Accepted Answer

The answer of Scores on a particular test have a...

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.

Accepted Answer

The answer of In one city, there are 1780 5-year...

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.

Accepted Answer

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

Question 20

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

Accepted Answer

The answer of Sample size = 400, sample mean =...

Quiz 8: From Samples to Populations

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.

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 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.