Exam 7: Sampling and Sampling Distributions

A random sample of size 36 is taken from a population with mean and standard deviation . Refer to Exhibit 7-5.What is the expected value and the standard deviation for the sampling distribution of the sample mean?

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

The finite correction factor is always _________________.

Which of the following is considered an estimate?

In any production process,variation in the quality of the end product is inevitable.Chance variation,or common variation,refers to ___________.

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 between 0.55 and 0.62 is __________.

A sample consists of all items of interest in a statistical problem,whereas a population is a subset of the population.We calculate a parameter to make inferences about the unknown sample statistic.

A tutoring company claims that 75% of the high school students who hire one of their tutor's 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 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.

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. Refer to Exhibit 7-9.What is the probability that from a sample of 200 Indianapolis residents,fewer than 170 were rooting for the Giants in Super Bowl XLIV?

For any population with expected value µ and standard deviation σ,the sampling distribution of will be approximately normal if the sample size n is sufficiently small.As a general guideline,the normal distribution approximation is justified when .

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 less than 0.55 is ________.

Statistics are used to estimate population parameters,particularly when it is impossible or too expensive to poll an entire population.A particular value of a statistic is referred to as a(n)_______.

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 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?

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 more than $50,000 but less than $60,000?

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 bottled water plant utilizes 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,and 21.1 ounces.Is the process under control?

Successful firms must focus on the quality of the products and services that they offer.Which factor(s)contributes to the quest for quality?

Selection bias occurs when ___________________.

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.What is the expected value and the standard deviation for a labor participation rate in the company's sample?