Exam 7: Sampling Distributions

All sampling plans involve random selection of the sample from the corresponding population.

When drawing all possible simple random samples of a given size n from a population, many different values of a sample statistic might occur. A listing of all these possible values, along with the associated probabilities of their occurrence, is called the statistic's:

When a sample is selected at random from a population, the sample mean will likely be:

A convenience sample is a sample that can be easily and simply obtained with random selection.

Once a process is in control and is producing a satisfactory product, the process variables are monitored by use of control charts.

The sample standard deviations measures the variability of all possible sample mean values that might be obtained.

Random cause variation refers to variation n, the output of a process that is unexpected and has an assignable cause.

In order to use the Central Limit Theorem to describe the sampling distribution of the sample mean , the sample size n must be 30 or more.

A recent nationwide survey by the American Cancer Society found the percentage of women who smoke has increased to 30%. That seems a little low for your state, so you sample 500 women from your state and find 180 of them smoke. Find the sample proportion of women who smoke in your state. ______________ Describe sampling distribution of ; the proportion of women who smoke. Is the sampling distribution approximately normal? ______________ What is the mean? ______________ What is the standard deviation? ______________ What is the probability that at least 36% of women in your state are smokers if the true population proportion p = 0.30? ______________ Does your answer to the previous question cast doubt on the American Cancer Society's claim? ______________

Quota sampling, in which the makeup of the sample must reflect the makeup of the population on some pre-selected characteristics, often has a nonrandom component in the selection process.

A population with a large standard deviation will have a sampling distribution that is more spread out for a given sample size than a similar population with a small standard deviation.

A statistics professor has stated that 90% of his students pass the class. To check this claim, a random sample of 150 students who have taken the class indicated that 129 passed the class. If the professor's claim is correct, what is the probability that 129 or fewer will pass the class this semester?

In a recent study, it was reported that the proportion of employees who miss work on Fridays is 0.15, and that the standard deviation of the sampling distribution of sample proportion is 0.025. However, the report did not indicate what the sample size n was. What was it?

Judgment sampling allows the sampler to decide who will or will not be included in the sample.

Suppose that 56% of all registered voters in Michigan are supporting John Kerry for president. A sample of 1500 voters is selected at random from Michigan. Based on the concept of sampling distribution of sample proportion , it can be assumed that = .56.

The mean of the sampling distribution of sample mean is equal to the mean of the population from which the samples are selected to construct the sampling distribution.

A machine which manufactures a part for a car engine was observed over a period of time before a random sample of 300 parts was selected from those produced by this machine. Out of the 300 parts, 15 were defective. Find the proportion of defective parts in the sample. ______________ Is the sampling distribution of the proportion of defectives approximately normal? ______________ What is the mean? ______________ What is the standard deviation? ______________ What is the probability that the sample proportion will lie within 0.02 of the true population proportion of defective parts? ______________

A well-known juice manufacturer claims that its citrus punch contains 15% real orange juice. A random sample of 150 cans of the citrus punch is selected and analyzed for content composition. 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 will be less than 0.10. ______________ Would a value of = 0.25 be considered unusual? ______________ Explain. ________________________________________________________

The Central Limit Theorem describes the distribution of the sample mean except for populations that are normal.

Random samples of size n were selected from populations with the means and variances given here. Find the mean and standard deviation of the sampling distribution of the sample mean in each case: a. n = 36, = 12, = 9 Mean: ______________ SD: ______________ b. n = 100, = 15, = 4 Mean: ______________ SD: ______________ c. n = 8, = 100, = 1 Mean: ______________ SD: ______________