Exam 7: Sampling and Sampling Distributions

Bias refers to the tendency of a sample statistic to systematically over- or underestimate a population parameter.

A random sample of size 100 is taken from a population described by the proportion . Refer to Exhibit 7-6.The probability that the sample proportion is greater than 0.62 is _______.

The central limit theorem states that,for any distribution,as n gets larger,the sampling distribution of the sample mean ____________.

According to the 2011 Gallup daily tracking polls (www.gallup.com,February 3,2012),Mississippi is the most conservative U.S.state,with 53.4 percent of its residents identifying themselves as conservative. Refer to Exhibit 7-10.What is the probability that at least 100 but fewer than 115 respondents of a random sample of 200 Mississippi residents identify as conservative?

The labor force participation rate is the number of people in the labor force divided by the number of people in the country that are of working age and not institutionalized.The BLS reported in February of 2012 that the labor force participation rate in the United States was 63.7% (Calculatedrisk.com).A marketing company asks 120 working-age people if they either have a job or are looking for a job,or,in other words,whether they are in the labor force. Refer to Exhibit 7-8.For the company's sample,the probability that the proportion of people who are in the labor force is greater than 0.65 is ___________.

According to the central limit theorem,the distribution of the sample means is normal if _______________.

Over the entire six years that students attend an Ohio elementary school,they are absent,on average,28 days due to influenza.Assume that the standard deviation over this time period is days.Upon graduation from elementary school,a random sample of 36 students is taken and asked how many days of school they missed due to influenza. Refer to Exhibit 7-1.What is the standard deviation for the sampling distribution of the number of school days missed due to influenza?

In a recent investigation,the National Highway Traffic Safety Administration (NHTSA)found that the Chevrolet Volt and other electric vehicles do not pose a greater risk of fire than gasoline-powered vehicles (The Boston Globe,January 25,2012).Specifically,it was determined that "no discernible defect trend exists." Suppose a consumer advocacy group wants to verify some of these claims by constructing a chart.The group expects 2% of electric cars to catch fire each month.For each of the last six months,500 electric car owners are asked if their cars have caught fire.The following sample proportions are obtained: 0.010 0.020 0.015 0.030 0.025 0.015 A)Assuming that the group expectation is correct,construct the centerline and the upper and lower control limits for the chart. B)Do the consumer group's findings support those of the NHTSA? Explain.

Which of the following is an example of a sample statistic?

A book publisher knows that it takes an average of nine business days from when the material for the book is finalized until the first edition is printed and ready to sell.Suppose the exact amount of time has a standard deviation of four days. A)Suppose the publisher examines the printing time for a sample of 36 books.What is the probability that the sample mean time is shorter than eight days? B)Suppose the publisher examines the printing time for a sample of 36 books.What is the probability that the sample mean time is between 7 and 10 days? C)Suppose the publisher signs a contract for the printer to print 100 books.If the average printing time for the 100 books is longer than 9.3 days,the printer must pay a penalty.What is the probability the penalty clause will be activated? D)Suppose the publisher signs a contract for the printer to print 10 books.If the average printing time for the 10 books is longer than 9.7 days,the printer must pay a penalty.What is the probability the penalty clause will be activated?

In a small town,there are 3,000 registered voters.An editor of a local newspaper would like to predict the outcome of the next election;in particular he is interested in the likelihood that Eli Brady will be elected.The editor believes that Eli,a local hero,will garner 54% of the vote.A poll of 500 registered voters is taken.Assuming that the editor's belief is true,calculate: A)The expected value and the standard deviation of the sample proportion. B)The probability that the sample proportion score is more than 0.58.

Suppose the average casino patron in Las Vegas loses $110 dollars per day,with a standard deviation of $700.Assume winnings/losses are normally distributed. A)What is the probability that a random group of nine people average more than $500 in winnings on their one day trip to Las Vegas? B)What is the probability that a random group of nine people average more than $500 in losses on their one day trip to Las Vegas?

For any population proportion p,the sampling distribution of will be approximately normal if the sample size n is sufficiently large.As a general guideline,the normal distribution approximation is justified when and .

Suppose that,on average,electricians earn approximately dollars per year in the United States.Assume that the distribution for electrician's yearly earnings is normally distributed and that the standard deviation is dollars. Refer to Exhibit 7-2.What is the probability that the average salary of four randomly selected electricians is less than $50,000?

Susan has been on a bowling team for 14 years.After examining all of her scores over that period of time,she finds that they follow a normal distribution.Her average score is 225,with a standard deviation of 13. Refer to Exhibit 7-3.If during a typical month Susan bowls 64 games,what is the probability that her average score in this month is above 227?

Nonresponse bias occurs when _________________.

A ski resort gets an average of 2,000 customers per weekday with a standard deviation of 800 customers.Assume the underlying distribution is normal.What is the probability a ski resort averages between 1,500 customers and 3,000 customers per weekday over the course of four weekdays?

A census is an example of __________.

A random sample of 49 cast aluminum pots is taken from a production line once every day.The number of defective pots is counted.The proportion of defective pots has been closely examined in the past and is believed to be 0.05. Refer to Exhibit 7-11.The sample proportions for the week are shown in the accompanying table. Is the production process in control?

The campaign manager for a candidate for governor in Arizona wants to conduct a poll to better understand his candidate's chances for the upcoming election. A)What is the population of interest? B)Why may the poll be biased if a simple random sample of voters in the last gubernatorial election (four years prior)is taken?