Exam 7: Sampling and Sampling Distributions

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 is the probability that fewer than 60% of those surveyed are members of the labor force?

A random sample of nine cast aluminum pots is taken from a production line once every hour.The interior diameter of the pots is measured and the sample mean is calculated.The target for the diameter is 12 inches and the standard deviation for the pot diameter is 0.05 inches.Assume the pot diameter is normally distributed.a.Construct the centerline and the upper and lower control limits for the chart.b.The means of the samples for a given eight-hour day are 12.01 12.06 11.97 12.08 11.92 11.95 11.97 12.04.Plot these values on the chart.c.Does it appear that the process is under control? Explain.

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

The detection approach to statistical quality control _______.

Suppose 35% of homes in a Miami,Florida,neighborhood are under water (in other words,the amount due on the mortgage is larger than the value of the home).There are 160 homes in the neighborhood and 30 of those homes are owned by your friends.What is the probability that fewer than 30% of your friends' homes are under water?

A local company makes snack-size bags of potato chips.The company produces batches of 400 snack-size bags using a process designed to fill each bag with an average of 2 ounces of potato chips.However,due to imperfect technology,the actual amount placed in a given bag varies.Assume the population of filling weights is normally distributed with a standard deviation of 0.1 ounce.The company periodically weighs samples of 10 bags to ensure the proper filling process.The last five sample means,in ounces,were 1.99,2.02,2.07,1.96,and 2.01.Is the production process under control?

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 40 Indianapolis residents,fewer than 95% were rooting for the Giants in Super Bowl XLIV?

According to the Bureau of Labor Statistics it takes an average of 16 weeks for young workers to find a new job.Assume that the probability distribution is normal and that the standard deviation is two weeks.What is the probability that 20 young workers average less than 15 weeks to find a job?A.0.0125

A random sample of size 36 is taken from a population with mean µ = 17 and standard deviation σ = 6.The probability that the sample mean is greater than 18 is _______.

A manufacturing process produces computer chips in batches of 100.The firm believes that the percent of defective computer chips is 2%.If in five batches the percent of chips defective were 3%,8%,1%,2%,and 7%,how many of these fell outside of the upper or lower control limits for the proportion of defective computer chips in a batch?

Using the central limit theorem,applied to the sampling distribution of the sample proportion,what conditions must be met?

A tutoring company claims that 75% of the high school students who hire one of their tutors will improve their grades.a.In a sample of 100 high school students,what is the probability that 80% or more improved their grades? b.In a sample of 200 high school students,what is the probability that 80% or more improved their grades? c.Comment on the reason for the difference between the computed probabilities in parts a and b.

A nursery sells trees of different types and heights.These trees average 60 inches in height with a standard deviation of 16 inches.Suppose that 75 pine trees are sold for planting at City Hall.What is the standard deviation for the sample mean?

A random sample of size 36 is taken from a population with mean µ = 17 and standard deviation σ = 6.The probability that the sample mean is between 15 and 18 is _______.

A bottled water plant uses a production process designed to fill bottles with 20 ounces of water.The population of filling volumes is normally distributed with a standard deviation of 1.3 ounces.Periodically,process engineers take 20-bottle samples and compute the sample mean. a.What are the upper and lower control limits? b.Suppose the last five sample means were 19.4 20.2 20.5 20.7 21.1 ounces.Is the process under control?

According to the recent report,scientists in New England say they have identified a set of genetic variants that predicts extreme longevity with 77% accuracy.Assume 150 patients decide to get their genome sequenced.If the claim by scientists is accurate,what is the probability that fewer than 70% of the patientswill get a correct diagnosis for extreme longevity?A.0.0207

A simple random sample is a sample of n observations that has the same probability of being selected from the population as any other sample of n observations.

A mining company made some changes to their mining process in an attempt to save fuel.Before the changes were made,it took an average of 20 gallons of diesel fuel to mine 1,000 pounds of copper.Suppose the standard deviation of fuel used per 1,000 pounds of copper mined is 6 gallons.After the changes were made,the company only used an average of 18 gallons of diesel for the next 30,000 pounds of copper mined.a.How unusual would it be to get a sample average of 18 gallons or less for 30,000 pounds of copper mined if the changes to the mining process had no effect? b.Do you think the changes in the mining process actually lowered the fuel used? Explain.

Which of the following is considered an estimator?

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 is the probability that between 60% and 62.5% of those surveyed are members of the labor force?