Exam 6: Sampling and Sampling Distributions

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: Suppose that 20% of all invoices are for amounts greater than $800.A random sample of 50 invoices is taken. -Based on the central limit theorem,the mean of all possible sample means is equal to the population:

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: Each member of a random sample of 20 business economists was asked to predict the rate of inflation for the coming year.Assume that the predictions for the whole population of business economists follow a normal distribution with standard deviation 2%. -Find the sampling distribution of sample means if all possible samples of size 2 are drawn with replacement from the following population:

The fraction of the population in the sample determines the precision of results from a random sample.

If all possible samples of size n are drawn from an infinite population with a mean μ and a standard deviation σ,then the standard error of the sampling distribution of sample mean is inversely proportional to:

The number of students using the ATM on campus daily is normally distributed with a mean of 237.6 and a standard deviation of 26.3.You take a random sample of 30 days.Find two values"a" and"b" that are symmetric around the mean such that the probability is 0.95 that the sample mean is greater than"a" and less than"b".

Determine the sampling distribution of sample means by listing all possible samples of 2 families that can be selected without replacement from this population.

If the standard error of the sampling distribution of the sample proportion is 0.02049 for samples of size 500,then the population proportion must be either:

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: A random sample of 10 stock market mutual funds was taken.Suppose that rates of returns on the population of stock market mutual funds follow a normal distribution. -Find any pair of numbers,a and b,to complete the following sentence: The probability is 0.95 that the sample variance is between a% and b% of the population variance.

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: According to the Internal Revenue Service,80% of all tax returns lead to a refund.A random sample of 100 tax returns is taken. -What is the mean of the sampling distribution of the sample proportion of returns leading to refunds?

It has been estimated that 53% of all college students change their major at least once during the course of their college career.Suppose you are told that the sample proportion for a random sample was 0.48.Furthermore,you are told that the probability of getting a sample proportion of this size or smaller is 14%.What must have been the sample size?

In a recent survey of college professors,it was found that the average amount of money spent on entertainment each week was normally distributed with a mean of $95.25 and a standard deviation of $27.32.What is the probability that the average spending of a sample of 25 randomly-selected professors will exceed $102.50?

If a sample of size 100 is taken from a population whose standard deviation is equal to 100,then the standard error of the mean is equal to:

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: Suppose that 20% of all invoices are for amounts greater than $800.A random sample of 50 invoices is taken. -What is the mean and standard error of the sample proportion of invoices with amounts in excess of $800?

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: A random sample of size n = 25 is obtained from a normally distributed population with population mean μ = 200 and variance σ² = 100. -What is the value of the sample variance such that 5% of the sample variances would be less than this value?

Acceptance intervals are widely used for quality control monitoring of various production and service processes.

As the size of the sample increases,what happens to the shape of the sampling distribution of sample means?

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: A store has determined that 28% of all refrigerators purchasers will also purchase a service agreement.In one month,250 refrigerators are sold to customers who can be regarded as a random sample of all purchasers. -What is the probability that the sample proportion will be less than 0.30?

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: Let the random variable X follow a normal distribution with a mean of μ and a standard deviation of σ.Let ₁ be the mean of a sample of 16 observations randomly chosen from this population,and ₂ be the mean of a sample of 25 observations randomly chosen from the same population. -Evaluate the statement P(μ - 0.2σ < ₁ < μ + 0.2σ)< P(μ - 0.2σ < ₂ < μ + 0.2σ)as to whether it is true or false.Please state if you are unable to determine whether the statement is true or false.Support your answer.

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: According to the Internal Revenue Service,80% of all tax returns lead to a refund.A random sample of 100 tax returns is taken. -What is the probability that the sample proportion is between 0.78 and 0.84?

Based on the sampling distribution of the means and the central limit theorem,the sample mean can be used as a good estimator of the population mean,assuming that the sample size,n,is sufficiently large.