Exam 7: Sampling Distributions

When drawing all possible simple random samples of a given size n from a population, many different values of a sample statistic might occur. What is the term for a listing of all these possible values, along with the associated probabilities of their occurrence?

As the sample size increases, the standard error of the sample mean decreases.

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

Stress and Sweets Narrative According to one study, 50% of Canadians admit to overeating sweet foods when stressed. Suppose that the 50% figure is correct and that a random sample of n = 100 Canadians is selected. -Refer to Stress and Sweets Narrative. What is the probability that the sample proportion, exceeds 0.54?

Which of the following is another name for assignable cause variation?

Department Store Audits Narrative 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. -Refer to Department Store Audits Narrative. Find the mean and standard deviation of the sampling distribution of .

The mean of the sampling distribution of the sample proportion, , when n = 100 and p = 0.5 is 5.0.

The expression SE represents the standard deviation of the sampling distribution of the sample proportion, .

Food Expenditures Narrative The amount of money spent on food per week by a Canadian family is known to have a mean of $92 and a standard deviation of $9. Suppose a random sample of 81 families is taken and their sample mean food expenditure is calculated. -Refer to Food Expenditures Narrative. Completely describe the sampling distribution of the sample mean, .

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

Lab Mice Experiments Narrative In a learning experiment, untrained mice are placed in a maze and the time required for each mouse to exit the maze is recorded. The average time for untrained mice to exit the maze is $\mu$ = 50 seconds and the standard deviation of their times is $\sigma$ = 16 seconds. Suppose that a sample of 64 randomly selected untrained mice are placed in the maze and the time necessary to exit the maze is recorded for each. -Refer to Lab Mice Experiments Narrative. Find the mean and standard deviation of the sampling distribution of .

Average Newborn Weights Narrative It is known that the birth weight of newborn babies in Canada has a mean of 3.20 kg with a standard deviation of 0.80 kg. Suppose we randomly sample 64 birth certificates and record the birth weights of these babies. -Refer to Average Newborn Weights Narrative. Find the mean and standard deviation of the sampling distribution of .

As a general rule, the normal distribution is used to approximate the sampling distribution of the sample proportion only if the sample size, n, is greater than or equal to 30.

On a particular highway in Nova Scotia, it is reported that the proportion of cars that exceed the speed limit is 0.15. Given this information, the probability that a sample of 250 cars will have a sample proportion below 0.12 is approximately 0.0918.

The expression SE represents the standard error sampling distribution of the sample proportion, .

A stratified random sample is chosen by taking separate (simple or systematic) random samples from every stratum, often in such a way that the sizes of the separate samples vary with the importance of the different strata.

Weights of Candy Bars Narrative A candy bar company is interested in reducing the percentage of defective candy bars made, where a defective candy bar is one that has too few almonds by weight. The company randomly samples 100 candy bars a day for 5 days and finds the percentage of the defective bars to be 0.0200, 0.0125, 0.0225, 0.0100, and 0.0150, respectively. The company wants to construct a control chart for the proportion defective in samples of size n = 100. -Refer to Weights of Candy Bars Narrative. Estimate the standard deviation of the sample proportions.

Small haphazard changes in a process variable due to alteration in the production environment that is not controllable are said to be assignable causes.

The spread of the distribution of sample means is considerably less than the spread of the sampled population.

The sampling distribution of the sample proportion, , can be approximated by a normal distribution as long as the population proportion, p, is very close to 0.50.