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 6713 students in one school district, 1578 cannot read up to grade level. Among a sample of 815 of the students from this school district, 210 cannot read up to grade level. Find the population proportion of students in this district who cannot read up to grade level.

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. - $E = 0.012$

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. - $E = 0.04$

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 40 and a standard deviation of 0.73. Suppose you take a random sample of 200 employees from the company and find that their mean age is 38.2. How many standard deviations is the sample mean from the mean of the distribution of sample means?

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 0.12. 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 0.54. This sample proportion lies 2.0 standard deviations above the mean of the sampling distribution. What is the probability that a second sample would be selected with a proportion Greater than 0.54 ?

A population proportion is to be estimated and a 95% degree of confidence is desired. In general, if one wishes to decrease the margin of error by a factor of 5 (for example from E = 0.05 to 0.01), by what numerical factor will the necessary sample size increase?

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 medical researcher wishes to estimate what proportion of babies born at a particular hospital are born by Caesarean section. In a random sample of 144 births at the hospital, 29\% were Caesarean sections. Find the $95 \%$ confidence interval for the population proportion.

The distribution of sample means for scores on a test for samples of size 100 is normal with a mean of 63.3 and a standard deviation of 1.5. If a sample of 100 test scores is selected at random, what is the probability that the sample mean will be less than 60.6?

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 1.3 hours. Past studies suggest that a population standard deviation of 13.6 hours is reasonable. Estimate the minimum sample size needed to estimate the population mean with the stated accuracy.

Find the population proportion or sample proportion as indicated. Round your answer to two decimal places, if necessary. -Of the 6660 students in one school district, 1590 cannot read up to grade level. Among a sample of 800 of the students from this school district, 198 cannot read up to grade level. Find the sample proportion of students who cannot read up to grade level.

The weights of five players on a football team are shown below. Player A B C D E Weight (lb) 290 320 250 255 220 Consider these five players to be a population. Construct a table which shows all of the possible samples of size two which can be selected without replacement. For each of the possible samples, list the players in the sample, their weights, and the sample mean $\bar { x }$ of the weights. The first line of the table is shown below. Sample Weights , 290,320 305 Use your table to find the mean of the sample means. Is this mean equal to the mean of the five given weights in the population?

Provide an appropriate response. -In a poll of 278 voters in a certain city, 65% said that they backed a bill which would limit growth and development in their city. The margin of error in the poll was reported as 6 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 the specified margin of error with a 95% degree of confidence. -A researcher wishes to estimate the proportion of adults living in rural areas who own a gun. He wishes to achieve a margin of error of 1.5%. What is the minimum sample size needed?

Solve the problem. -Among a random sample of 150 employees of a particular company, the mean commute distance is 29.5 miles. This mean lies 2.2 standard deviation(s)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 less than 29.5 miles?

Solve the problem. -Among a random sample of 150 employees of a particular company, the mean commute distance is 26.8 miles. This mean lies 2.7 standard deviation(s)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 26.8 miles?

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 $12. Past studies suggest that a population standard deviation of $229 is reasonable. Estimate the minimum sample size needed to estimate the population mean with the stated accuracy.

At one hospital, a random sample of 100 women giving birth to their first child is selected. Among this sample, the mean age was $25.6$ with a standard deviation of $5.9$ . Find the $95 \%$ confidence interval. Round your answer to two decimal places.

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 140 residents is normal with a mean of 0.12 and a standard deviation of 0.02. Suppose that you select a sample of 140 residents and find that the proportion of residents over 70 is 0.04. How many standard deviations is the sample proportion above or below the mean of the distribution of sampling proportions?

A researcher wishes to estimate the proportion of left-handed people among a certain population. In a random sample of 1000 people from the population, 68.3% are left-handed. Find the margin of error for the 95% confidence interval.

Solve the problem. Round your answer to one decimal place, if necessary. -A random sample of 30 households was selected from a particular neighborhood. The number of cars for each household is shown below. Find the 95% confidence interval for the mean number of cars per household for the Population of households in this neighborhood. 2 0 1 2 3 2 1 0 1 4 1 3 2 0 1 1 2 3 1 2 1 0 4 1 3 2 2 1 0 2