Exam 7: Sampling Distributions

The shape of the normal distribution is determined by its mean and its standard deviation .

Suppose that college faculty with the rank of professor at 4-year institutions earn an average of $72,500 per year with a standard deviation of $4500. In an attempt to verify this salary level, a random sample of 60 professors was selected from a personnel database for all 4-year institutions in the United States. Is the sampling distribution of the sample mean approximately normal? ______________ What is the mean? ______________ What is the standard deviation? ______________ Within what limits would you expect the sample average to be, with probability 0.95? Lower - $ ______________ Upper - $ ______________ Calculate the probability that the sample mean is greater than $75,000. ______________ If your random sample actually produced a sample mean of $75,000, would you consider this unusual? ______________ What conclusion might you draw? ________________________________________________________

The first objective in statistical process control is to eliminate assignable causes of variation in the process variable and then get the process in control. The next step is to reduce variation and get the measurements on the process variable within specification limits, the limits within which the measurements on usable items or services must fall.

Which of the following statements is true regarding the sampling distribution of sample proportion ?

If a population standard deviation is equal to 50, then the sampling distribution of the sample mean will have a standard deviation that is less than 50 for all samples of size n 2.

The dean of admissions in a large university has determined that the scores of the freshman class in a mathematics test are normally distributed with a mean of 82 and a standard deviation of 8. Based on this information, what is the probability that the mean score of a sample of 64 students is at least 80?

The population of Pepsi cans filled by a particular machine is known to be normally distributed with a mean of 12 ounces and a standard deviation of.16 ounces. Given this information, the sampling distribution of the sample mean for a random sample of 16 cans will also be normally distributed with a standard deviation equal to .04.

A study of an experimental blood thinner was conducted to determine whether it works better than the simple aspirin tablet in warding off heart attacks and strokes. The study involved 20,000 people who had suffered heart attacks, strokes, or pain from clogged arteries. Each person was randomly assigned to take either aspirin or the experimental drug for 1 to 3 years. Assume that each person was equally likely to be assigned one of the two medications. Devise a randomization plan to assign the medications to the patients. ________________________________________________________ Will there be an equal number of patients in each treatment group? Explain. ________________________________________________________

If a process is in control, we expect all the data values to fall within two standard deviations of the mean.

Nonrandom samples can be described and also be used for making inferences.

The dean of admissions in a large university has determined that the scores of the freshman class in a mathematics test are normally distributed with a mean of 82 and a standard deviation of 8. Based on this information, what is the standard deviation of the sampling distribution of the sample mean if a sample of 64 students is selected at random from the entire freshman class?

A student government representative at a local university claims that 60% of the undergraduate students favor a move to Division I in college football. A random sample of 250 undergraduate students is selected. Is the sampling distribution of the sample proportion approximately normal? ______________ What is the mean? ______________ What is the standard deviation? ______________ Find the probability that the sample proportion exceeds 0.65. ______________

The standard error of the sampling distribution of sample proportion, SE ( ), depends on the value of the population proportion p, and the closer the value of p to .50, the larger SE ( ) will be for a given sample size n.

If random samples of size n = 50 are drawn from a nonnormal population with finite mean =100 and standard deviation = 20, then, the sampling distribution of the sum of sample measurements is approximately normally distributed with mean and standard deviation .

According to the Central Limit Theorem, for large samples the standard error of the sample mean is the population standard deviation divided by the square root of the sample size.

The dean of admissions in a large university has determined that the scores of the freshman class in a mathematics test are normally distributed with a mean of 82 and a standard deviation of 8. Based on this information, what is the mean of the sampling distribution of the sample mean if a sample of 64 students is selected at random from the entire freshman class?

In most processes, the process control limits are set to correspond with the specification limits on the process.

The mean lifetime of a fluorescent light bulb is 1,570 hours with a standard deviation of 200 hours. Suppose we take a sample of 100 bulbs, test them, and calculate the sample mean. Find the mean of the sampling distribution. ______________ Find the standard deviation. ______________ What is the probability the sample mean exceeds 1,560 hours? ______________

An auditor is going to sample 64 charge accounts from the many active accounts at a large department store. Suppose the average balance owed among all the store's accounts is $75 with a standard deviation of $100. Find the mean of the sampling distribution of . ______________ Find the standard deviation. ______________ What is the probability the sample mean of the balances owed among the 64 accounts sampled by the auditor is below $70? ______________

Which of the sample sizes below will produce a sampling distribution of the mean that is approximately normal?