Exam 7: Sampling and Sampling Distributions

The College Student Journal (December 1992)investigated differences in traditional and nontraditional students,where nontraditional students are defined as 25 years old or older and working.Based on the study results,we can assume the population mean and standard deviation for the GPA of nontraditional students is µ = 3.5 and σ = 0.5.Suppose a random sample of 100 nontraditional students is selected and each student's GPA is calculated.What is the probability that the random sample of 100 nontraditional students has a mean GPA greater than 3.42?

Methods for obtaining a sample are called:

It has been reported that the average time to download the home page from a government website was 0.9 seconds.Suppose that the download times were normally distributed with a standard deviation of 0.3 seconds.If random samples of 36 download times are selected,80 percent of the sample means will be between what two values symmetrically distributed around the population mean?

When we perform ______________,an element of a population always has a chance of being chosen at each point of selection.

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 13 percent of the accounts have been delinquent.For this quarter,the auditing staff randomly selected 250 customer accounts.What is the probability that no more than 40 accounts will be classified as delinquent?

A recording error is an error of observation.

A random sample of size 1,000 is taken from a population where p = .20.Find $\mathrm { P } ( \hat { p } > .21 )$

A random sample of size 36 is taken from a population with a mean of 50 and a standard deviation of 5.The sampling distribution of $\bar { X }$ ____________________.

For any sampled population,the population of all sample means is approximately normally distributed.

A random sample of size 36 is taken from a population with mean 50 and standard deviation 5.Find $\mathrm { P } ( \bar { X } < 48 )$

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 are the mean and the standard deviation of the sampling distribution of $\hat { p }$ ?

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

In the upcoming governor's election,the most recent poll,based on 900 respondents,predicts that the incumbent will be reelected with 55 percent of the votes.From the 900 respondents,how many indicated that they would not vote for the current governor or indicated that they were undecided?

Nonoverlapping groups in random sampling of a population are called:

Suppose that 60 percent of the voters in a particular region support a candidate.Find the probability that a sample of 1,000 voters would yield a sample proportion in favor of the candidate within 2 percentage points.

The population of all sample proportions has a normal distribution if the sample size (n)is sufficiently large.The rule of thumb for ensuring that n is sufficiently large is:

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 standard deviation of the sampling distribution of the sample mean?

A random sample of size 36 is taken from a population with mean 50 and standard deviation 5.Find $\mathrm { P } ( \bar { X } > 50.5 )$

_____________ is the difference between a numerical description of the population and the corresponding descriptor of the sample.

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 most 3.1 inches?