Exam 6: Sampling and Sampling Distributions

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 greater than this value?

If the standard error of the sampling distribution of sample proportions is 0.0245 for samples of size 400,then the population proportion must be 0.40.

What is the name of the parameter that determines the shape of the chi-square distribution?

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 are the mean and standard deviation of the sampling distribution for the sample means?

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 probability that more than 22.7% of these 50 invoices are for more than $800?

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: In taking a sample of n observations from a population of N members,the variance of the sampling distribution of the sample means is = .The quantity is called the finite population correction factor. -To get some feeling for possible magnitudes of the finite population correction factor,calculate it for samples of n = 15 observations from populations of N = 15,30,60,100,500,1,000,5,000,and 10,000 members.

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: Suppose you flip a coin four times.For every head,you receive one point,and for every tail,you lose one point. -Develop the sampling distribution for the mean number of points you receive from flipping four coins.

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. -Suppose that 15% of all invoices are for amounts greater than $1,000.A random sample of 60 invoices is taken.What is the mean and standard error of the sample proportion of invoices with amounts in excess of $1,000? What is the probability that the proportion of invoices in the sample is greater than 18%?

Why is the central limit theorem important to statistical analysis?

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. -The probability is 0.10 that sample variance is bigger than what percentage of the population variance?

The variance of the sampling distribution of sample mean decreases as the sample size,n,increases.

The central limit theorem can be applied to both discrete and continuous random variables.

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 exceeds 0.85?

Without doing the calculations,state in which of the following ranges the sample mean selling price is most likely to lie:

If the sample size,n,equals the population size,N,then the variance of the sample mean, ,is zero.

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: A sample of 25 bottles is taken from the production line at a local bottling plant.Assume that the fill amounts follow a normal distribution. -The probability is 90% that the sample variance is less than what percent of the population variance?

All possible random samples of 200 middle managers are selected from a population for a study concerning their mean annual income.The population standard deviation is computed to be $2,248.5.What is the standard deviation of the sampling distribution of the means?

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: Monthly rates of return on the shares of a particular common stock are independent of one another and normally distributed with a standard deviation of 1.8.A sample of 15 months is taken. -Find the probability that the sample standard deviation is less than 2.6.

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: The mean selling price of new homes in a city over a year was $120,000.The population standard deviation was $28,000.A random sample of 100 new home sales from this city was taken. -What is the probability that the sample mean selling price was between $119,000 and $121,000?

The length of time it takes for a stock analyst to complete an evaluation of a company's earnings forecast is normally distributed with a standard deviation of 1.7 hours.From looking at the time spent by an analyst evaluating 15 randomly-selected stocks you find that the sample mean was 6.4 hours.If you know that the probability of getting a sample mean this large or larger is 0.36,what is the mean of the population?