Exam 8: From Samples to Populations

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.

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 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.

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.

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?

Sample size $=100$ , sample mean $=39$ , sample standard deviation $=13$ . What is the $95 \%$ confidence interval for the population mean?

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.

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?

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

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?

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.

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.

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.

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.

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. 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

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?

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.

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.

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.

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.