Exam 7: Sampling and Sampling Distributions

Nonresponse bias occurs when those responding to a survey or poll differ systematically from the nonrespondents.

Suppose that, on average, electricians earn approximately µ = $54,000 per year in the United States. Assume that the distribution for electricians' yearly earnings is normally distributed and that the standard deviation is σ = $12,000. What is the probability that the average salary of four randomly selected electricians is less than $50,000?

John would like to conduct a survey in his neighborhood to get homeowners' opinion on Delmarva proposal to switch to natural gas. Which of the following is an example of a stratified sample?

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 200 Indianapolis residents, fewer than 170 were rooting for the Giants in Super Bowl XLVI?

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 XLVI?

The central limit theorem approximation improves as the sample size decreases.

When a statistic is used to estimate a parameter, the statistic is referred to as an estimator. A particular value of the estimator is called an estimate.

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 (standard error) of the sample proportion. B) The probability that the sample proportion score is more than 0.58.

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. The probability that the sample mean is between 25 and 30 school days is ________.

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 local company makes snack-size bags of potato chips. Each day, 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 amount placed in each of the 400 bags is normally distributed and has a standard deviation of 0.1 ounce. What is the probability that a sample of 40 bags has an average weight of at least 2.02 ounces?

Which of the following is true about statistics such as the sample mean or sample proportion?

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. If during a typical week Susan bowls 16 games, what is the probability that her average score for the week is between 220 and 228?

Which of the following is not a form of bias?

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?

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 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?

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?

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 less than 15 is ________.

A school is required by the government to give some randomly chosen students a standardized test. From previous experience, the school knows about 68% of their students will receive passing scores in math and English. To improve funding, the school needs to score at least 70% on the standardized test. This year the school can decide if it wants to test 100 or 200 students. Should the school test 100 or 200 students? Explain the answer.