Exam 7: Introduction to Sampling Distributions

The proportion of items in a population that possess a specific attribute is known to be 0.70.If a simple random sample of size n = 100 is selected and the proportion of items in the sample that contain the attribute of interest is 0.65,what is the sampling error?

Which of the following statements is true with respect to the sampling distribution of a proportion?

The proportion of parts in an inventory that are outdated and no longer useful is thought to be 0.10.To check this,a random sample of n = 100 parts is selected and 14 are found to be outdated.Based upon this information,what is the probability of 14 or more outdated parts?

A population has a proportion equal to 0.30.Calculate the following probabilities with n = 100.Find P( > 0.40).

The J R Simplot Company is one of the world's largest privately held agricultural companies,employing over 10,000 people in the United States,Canada,China,Mexico,and Australia.More information can be found at the company's Web site: www.Simplot.com.One of its major products is french fries that are sold primarily on the commercial market to customers such as McDonald's and Burger King.French fries have numerous quality attributes that are important to customers.One of these is called "dark ends," which are the dark-colored ends that can occur when the fries are cooked.Suppose a major customer will accept no more than 0.06 of the fries having dark ends. Recently,the customer called the Simplot Company saying that a recent random sample of 300 fries was tested from a shipment and 27 fries had dark ends.Assuming that the population does meet the 0.06 standard,what is the probability of getting a sample of 300 with 27 or more dark ends?

If a population is not normally distributed,then the sampling distribution for the mean also cannot be normally distributed.

Suppose nine items are randomly sampled from a normally distributed population with a mean of 100 and a standard deviation of 20.The nine randomly sampled values are: Calculate the probability of getting a sample mean that is smaller than the sample mean for these nine sampled values.

Given a population in which the probability of success is p =0.20,if a sample of 500 items is taken,then calculate the probability the proportion of successes in the sample will be between 0.18 and 0.23.

In analyzing the sampling distribution of a proportion,doubling the sample size will cut the standard deviation of the sampling distribution in half.

The reason that a population mean and the mean of a random sample selected from that population might be different is that the sample mean is found by dividing by n-1 while the population mean is found by dividing by n.

According to the local real estate board,the average number of days that homes stay on the market before selling is 78.4 with a standard deviation equal to 11 days.A prospective seller selected a random sample of 36 homes from the multiple listing service.Above what value for the sample mean should 95 percent of all possible sample means fall?

A major textbook publisher has a contract with a printing company.Part of the contract stipulates that no more than 5 percent of the pages should have any type of printing error.As a quality control measure,the publisher periodically selects a random sample of n = 100 pages.Then,depending on the proportion of pages with errors,they either say nothing to the printer or they complain that the quality has slipped.Suppose the publisher wants no more than a .10 chance of mistakenly blaming the printer for poor quality,what should the cut-off proportion be?

Which of the following statements is not consistent with the Central Limit Theorem?

If the monthly electrical utility bills of all customers for the Far East Power and Light Company are known to be distributed as a normal distribution with mean equal to $87.00 a month and standard deviation of $36.00,which of the following would be the largest individual customer bill that you might expect to find?

Which of the following statements is false?

The National Association of Realtors released a survey indicating that a surprising 43% of first-time home buyers purchased their homes with no-money-down loans during 2005.The fear is that house prices will decline and leave homeowners owing more than their homes are worth.PMI Mortgage Insurance estimated that there existed a 50% risk that prices would decline within two years in major metro areas such as San Diego,Boston,Long Island,New York City,Los Angeles,and San Francisco.A survey taken by realtors in the San Francisco area found that 12 out of the 20 first-time home buyers sampled purchased their home with no-money-down loans.Calculate the probability that at least 12 in a sample of 20 first-time buyers would take out no-money-down loans if San Francisco's proportion is the same as the nationwide proportion of no-money-down loans.

A golf course in California has determined that the mean time it takes for a foursome to complete an 18 hole round of golf is 4 hours 35 minutes (275 minutes)with a standard deviation of 14 minutes.The time distribution is also thought to be approximately normal.Every month,the head pro at the course randomly selects a sample of 8 foursomes and monitors the time it takes them to play.Suppose the mean time that was observed for the sample last month was 4 hours 44 minutes (284 minutes).What is the probability of seeing a sample mean this high or higher?

An increase in sample size will tend to result in less sampling error.

The population of incomes in a particular community is thought to be highly right-skewed with a mean equal to $36,789 and a standard deviation equal to $2,490.Based on this,if a sample of size n = 36 is selected,the highest sample mean that we would expect to see would be approximately $38,034.

A sample proportion can be assumed normally distributed if n ≥ 30.