Exam 7: Sampling and Sampling Distributions

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 exceeds $60,000?

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

What is the relationship between the expected value of the sample mean and the expected value of the population?

A large accounting firm gives out 1,000 job offers every year to new college graduates.Suppose that 85% of those that received offers accept the position.The following shows the number of graduates that have accepted jobs in the last four years. Number of job offers accepted:

Professor Elderman has given the same multiple choice final exam in his Principles of Microeconomics class for many years.After examining his records from the past 10 years,he finds that the scores have a mean of 76 and a standard deviation of 12. Refer to Exhibit 7-4.What is the probability that a class of 36 students will have an average greater than 70 on Professor Elderman's final exam?

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.

The detection approach to statistical quality control ____________.

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.What is the probability that in a one-game playoff,her score is more than 227?

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.

Which of the following is not a population parameter?

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

It is known that college students at a local community college study 12 hours per week with a standard deviation of 5 hours.What is the expected value and variance for a sample of nine students?

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:

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

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

The standard deviation of equals the population standard deviation divided by the square root of the sample size,or equivalently, .

Professor Elderman has given the same multiple choice final exam in his Principles of Microeconomics class for many years.After examining his records from the past 10 years,he finds that the scores have a mean of 76 and a standard deviation of 12. Refer to Exhibit 7-4.What is the probability Professor Elderman's class of 36 has a class average below 78?

Which of the following is not a form of bias?

Bias can occur in sampling.Bias refers to _____________________.

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' and the standard deviation for the pot diameter is 0.05'.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,and 12.04.Plot these values on the chart. C)Does it appear that the process is under control? Explain.