Exam 8: Inferences From Samples to Populations

Find the population proportion or sample proportion as indicated. Round your answer to two decimal places, if necessary. -Of the 2393 students at a liberal arts college, 247 are fifth year students. Among a sample of 316 of the students from this college, 37 are fifth year students. Find the sample proportion of fifth year students.

A population mean is to be estimated from the sample described. Round your answer to one decimal place if necessary. Assume that all confidence intervals use a 95% confidence level. -Sample size = 3025, sample mean = 244, sample standard deviation = 80 What is the margin of error?

A population proportion is to be estimated. Estimate the minimum sample size needed to achieve the specified margin of error with a 95% degree of confidence. - $\mathrm { E } = 0.013$

Find the population proportion or sample proportion as indicated. Round your answer to two decimal places, if necessary. -Of the 9260 registered voters in one town, 4681 are women. Among a sample of 539 of the registered voters from this town, 265 are women. Find the sample proportion of registered voters who are women.

There are 13,259 eligible voters in one town. In a sample of 833 eligible voters from this town, 394 say that they plan to vote in the next mayoral election. Based on this sample statistic, estimate the number of eligible voters in This town who will vote in the next mayoral election.

Find an estimate of the sample size needed to obtain the specified margin of error for the 95% confidence interval of a population mean. -Margin of error $= 28$ , sample standard deviation $= 300$

Solve the problem. -Suppose you know that the distribution of sample proportions of fifth grade students in a large school district who read below grade level in samples of 100 students is normal with a mean of 0.30 and a standard deviation of 0.04. Suppose that you select a sample of 100 fifth grade students from this district and find that the proportion who read below grade level in the sample is 0.4. What is the probability that a second sample would be selected with a proportion less than 0.4 ?

Sample size $= 2500$ , sample mean $= 223$ , sample standard deviation $= 96$ What is the $95 \%$ confidence interval for the population mean?

Find the population proportion or sample proportion as indicated. Round your answer to two decimal places, if necessary. -Of the 9238 registered voters in one town, 4694 are women. Among a sample of 540 of the registered voters from this town, 262 are women. Find the population proportion of registered voters who are women.

Solve the problem. -Among a random sample of 400 college students, the mean number of hours worked per week at non-college related jobs is 14.4. This mean lies 2.8 standard deviation(s)above the mean of the sampling distribution. If a second sample of 400 students is selected, what is the probability that for the second sample, the mean number of hours worked will be less than 14.4?

Solve the problem. Round your answer to one decimal place, if necessary. -The distribution of sample means for the ages of employees at a particular company for samples of 200 employees is normal with a mean of 39 and a standard deviation of 0.62. Suppose you take a random sample of 200 employees from the company and find that their mean age is 39.8. How many standard deviations is the sample mean from the mean of the sampling distribution?

There are 341 teachers at a college. In a sample of 110 teachers from this college, 72 have doctorates. Based on this sample statistic, estimate the number of teachers at this college with doctorates.

A population proportion is to be estimated from the sample described. Approximate the 95% confidence interval. Round your answer to four decimal places, if necessary. -A poll of 1300 voters in one district showed that $55 \%$ of them would favor stricter gun control laws. Find the $95 \%$ confidence interval for the population proportion favoring stricter gun control laws.

Solve the problem. -Suppose you know that the distribution of sample proportions of the residents of one town over 70 years old in samples of 110 residents is normal with a mean of 0.12 and a standard deviation of 0.02. You select a sample of 110 residents and find that the proportion of residents over 70 is 0.08. The standard score corresponding to this sample proportion is -2. What is the probability that a second sample would be selected with a proportion less Than 0.08?

A laboratory tested 78 chicken eggs and found that the mean amount of cholesterol was 224 milligrams with $s = 14.7$ milligrams. Find the $95 \%$ confidence interval.

A mayoral election race is tightly contested. In a random sample of 2300 likely voters, 1219 said that they were planning to vote for the current mayor. Based on this sample, would you claim that the mayor will win a majority of the votes? Explain.

Suppose that a researcher wants to consider the average income of the three largest states in the country. consider these three states to be the entire population from which samples will be selected with replacement. The researcher finds the distribution of sample means for sample sizes n = 1, 2, and 3. Then she finds the means of the distributions of sample means for n = 1, 2, and 3. Compare the means of the distributions of sample means to the population mean.

A population proportion is to be estimated from the sample described. Approximate the margin of error for the 95% confidence interval. Round your answer to four decimal places, if necessary. -Sample size $= 1600$ , sample proportion $= 0.93$

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 2.2 mmHg. Past studies suggest that a population standard deviation of 42 mmHg is reasonable. Estimate the minimum sample size needed to estimate the population mean with the stated accuracy.

Solve the problem. Round your answer to one decimal place, if necessary. -The distribution of sample means for monthly employee income at a particular company for samples of 70 employees is normal with a mean of $5921 and a standard deviation of $219. You take a random sample of 70 employees from the company and find that their mean monthly income is $5668. How many standard deviations is the sample mean from the mean of the distribution of sample means?