Exam 8: Sampling Distributions

A research study investigated differences between male and female students. Based on the study results, we can assume the population mean and standard deviation for the GPA of male students are µ = 3.5 and σ = .5. Suppose a random sample of 100 male students is selected and the GPA for each student is calculated. Find the interval that contains 95.44 percent of the sample means for male students.

The notation for the standard deviation of the sampling distribution of the sample mean is ________.

The number of defectives in 10 different samples of 100 observations each is the following: 1, 2, 1, 0, 2, 3, 1, 4, 2, 1. What is the estimate of the population proportion of defectives?

In a manufacturing process, a machine produces bolts that have an average length of 3 inches with a variance of .03. If we randomly select three bolts from this process, what is the probability the mean length of the bolt is at least 3.16 inches?

A random sample of size 36 is taken from a population with mean 50 and standard deviation 5. What is μ_x?

If we have a sample size of 100 and the estimate of the population proportion is .10, what is the standard deviation of the sampling distribution of the sample proportion?

In the upcoming election for governor, the most recent poll, based on 900 respondents, predicts that the incumbent will be reelected with 55 percent of the votes. What is ?

The population of lengths of aluminum-coated steel sheets is normally distributed with a mean of 30.05 inches and a standard deviation of .3 inches. What is the probability that the average length of a steel sheet from a sample of 9 units is more than 29.95 inches long?

The sampling distribution of a sample statistic is the probability distribution of the population of all possible values of the sample statistic.

The diameter of small Nerf balls manufactured overseas is expected to be approximately normally distributed with a mean of 5.2 inches and a standard deviation of .08 inches. Suppose a random sample of 20 balls is selected. Calculate the mean of the sampling distribution of the sample mean.

A research study investigated differences between male and female students. Based on the study results, we can assume the population mean and standard deviation for the GPA of male students are µ = 3.5 and σ = .5. Suppose a random sample of 100 male students is selected and the GPA for each student is calculated. Calculate .

It has been reported that the average time to download the home page from a government website was .9 seconds. Suppose that the download times were with a standard deviation of .3 seconds. If random samples of 23 download times are selected, describe the shape of the sampling distribution and how it was determined.

A random sample of size 36 is taken from a population with mean 50 and standard deviation 5. What is ?

The internal auditing staff of a local manufacturing company performs a sample audit each quarter to estimate the proportion of accounts that are more than 90 days overdue (delinquent). The historical records of the company show that over the past 8 years, the average has been that 14 percent of the accounts have been delinquent. For this quarter, the auditing staff randomly selected 250 customer accounts. What is the probability that at least 30 accounts will be classified as delinquent?

As the sample size increases, the variability of the sampling distribution of the mean ________.

A research study investigated differences between male and female students. Based on the study results, we can assume the population mean and standard deviation for the GPA of male students are µ = 3.5 and σ = .5. Suppose a random sample of 100 male students is selected and the GPA for each student is calculated. What is

Find σ_x, if μ = 400, P( < 396) = .0228, and n = 100.

If a population is known to be normally distributed, then the single sample mean must equal the population mean.

For large samples, the sampling distribution of is approximately normal with a mean of ________.

The diameter of small Nerf balls manufactured overseas is expected to be approximately normally distributed with a mean of 5.2 inches and a standard deviation of .08 inches. Suppose a random sample of 20 balls is selected. Find the interval that contains 95.44 percent of the sample means.