Exam 7: Sampling and Sampling Distributions

In a large metropolitan area,the top providers for television and Internet services are a phone company,a satellite company,and a cable company.The satellite company serves 43% of the homes in the area.What is the probability that in a survey of 1,000 homes,more than 447 of them are served by the satellite company?

A large accounting firm gives out 1,000 job offers every year to new college graduates.Suppose that 85% of those who received offers accept the position.The following shows the number of graduates who have accepted jobs in the last four years.Number of job offers accepted: a.Construct the centerline and the upper and lower control limits for the chart. b.Does the company need to worry about its ability to attract college graduates to the firm?

Super Bowl XLVI was played between the New York Giants and the New England Patriots in Indianapolis.Due to a decade-long rivalry between the Patriots and the city's own team,the Colts,most Indianapolis residents were rooting heartily for the Giants.Suppose that 90% of Indianapolis residents wanted the Giants to beat the Patriots.What is the probability that from a sample of 100 Indianapolis residents,fewer than 95% were rooting for the Giants in Super Bowl XLVI?

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

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.What is the probability that at least 60% of a random sample of 200 Mississippi residents identify themselves as conservative?

The finite correction factor is always _______.

What is the relationship between the standard deviation of the sample mean and the population standard deviation?

The _______ _____ of is the same as the mean of the individual observations.

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.What are the upper and lower control limits for the chart?

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 np ≥ 5 and n(1 −p)≥ 5.

If the expected value of a sample mean equals the population mean,the sample mean is biased.

Suppose the local Best Buy store averages 522customers every day entering the facility with a standard deviation of 124 customers.A random sample of 40 business days was selected.What is the probability that the average number of customers in the sample is between 530 and 540?

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?

The labor force participation rate is the number of people in the labor force divided by the number of people in the country who are of working age and not institutionalized.The BLS reported in February 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.What are the expected value and the standard error for a labor participation rate in the company's sample?

A manufacturing process produces tubeless mountain bike tires in batches of 200.Past records show that 6% of the tires will not hold air.An engineer tests five batches,each one week apart,and shows the proportion of tires that will not hold air below.Proportion of tires that will not hold air: a.Construct the centerline and the upper control limit for the chart. b.Should the engineer be worried? Comment on any trend in the proportion of tubeless tires that will not hold air.

A packaging company strives to maintain a constant temperature for its packages that require a specific temperature range.It is believed that the temperature of packages follows a normal distribution with a mean of 5 degrees Celsius and a standard deviation of 0.3 degree Celsius.Inspectors take weekly samples for five weeks of eight randomly selected boxes and report their temperatures.The five weekly sample means are shown in the table below. How many points are outside the control limits?

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 σ = 9 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.What is the standard deviation for the sampling distribution of the number of school days missed due to influenza?

In any production process,variations in the quality of the end product are inevitable.Assignable variation refers to _______.

A parameter is a random variable,whereas a sample statistic is a constant.

A random sample of size 100 is taken from a population described by the proportion p = 0.60.What are the expected value and the standard error for the sampling distribution of the sample proportion?