Exam 8: From Samples to Populations

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?

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?

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.

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.

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.

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 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

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

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.

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.

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?

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 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?

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.

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

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%?

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?

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 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.

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?