Exam 7: Sampling Distributions

The stratified random sample is a subset of a population, chosen by randomly selecting one of the first k elements and then including every kth element thereafter until the desired sample size has been reached.

Childcare Amounts Paid Narrative The distribution of the amount spent for childcare in a city has a mean of $675 and a standard deviation of $80. A random sample of 64 families paying for childcare is selected. -Refer to Childcare Amounts Paid Narrative. Find the probability that the sample mean is less than $700.

A group of people who, in response to some general appeal, have selected themselves to participate in a survey is called a simple random sample.

Fuel Consumption of Cars Narrative Suppose the average fuel consumption (in litres per 100 km) of a particular model car is 8.4 L/100 km with a standard deviation of 2.4 L/100 km. A random sample of 64 cars of this model is selected. -Refer to Fuel Consumption of Cars Narrative. What is the probability that the sample mean exceeds 9.0 L/100 km?

As a general rule, the normal distribution provides a good approximation to the sampling distribution of the sample proportion, , only if which of the following conditions holds?

There are four ways of selecting a distinct, unordered sample of size n = 2 without replacement from a population of size N = 4.

Defective Items Narrative Suppose a sample of 120 items is drawn from a population of manufactured products and the number of defective items is recorded. Prior experience has shown that the proportion of defectives is 0.05. -Refer to Defective Items Narrative. How would the sampling distribution of the sample proportion change if the sample size were raised to 200?

Defective Engine Parts Narrative A machine that 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. Of the 300 parts, 15 were defective. -Refer to Defective Engine Parts Narrative. What is the probability that the sample proportion will lie within 0.02 of the true population proportion of defective parts?

Canadian Cancer Society Survey Narrative A recent nationwide survey by the Canadian Cancer Society found the percentage of women who smoke has increased to 30%. That seemed a little low for your province, so you sampled 500 women from your province and found that 180 of them smoke. -Refer to Canadian Cancer Society Survey Narrative. What is the probability that at least 36% of women in your province are smokers if the true population proportion p = 0.30?

The publisher of a newspaper decides which articles will be submitted for the consideration of the Pulitzer Prize committee. This is an example of cluster sampling.

The c chart is another commonly used process control chart that is used to monitor the number of defects per item in that process.

NHL Stanley Cup Finals Narrative A TV pollster believed that 70% of Canadian TV households would be tuned in to Game 5 of the 2008 NHL Stanley Cup series between the Pittsburgh Penguins and the Detroit Red Wings. A random sample of 500 TV households is selected. -Refer to NHL Stanley Cup Finals Narrative. Completely describe the sampling distribution of the sample proportion.

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

Salaries of Professors Narrative Suppose that college faculty with the rank of professor at four-year institutions earn an average of $72,500 per year with a standard deviation of $4,500. In an attempt to verify this salary level, a random sample of 60 professors was selected from a personnel database for all four-year institutions in Canada. -Refer to Salaries of Professors Narrative. Describe the sampling distribution of the sample mean .

Given N = 1000, n = 30, and = 6, what is the standard error of the sample mean, SE ?

A sampling distribution is a probability distribution that shows the likelihood of occurrence associated with all the possible values of a parameter whose values would be obtained when drawing all possible samples of a given size from a population.

Assignable cause variation refers to variation in the output of a process that is naturally occurring and expected, and that may be the result of random causes.

Consider a large population with a mean of 150 and a standard deviation of 27. A random sample of size 36 is taken from this population. Which of these values is equal to the standard error of the sampling distribution of sample mean?

What are some of the most common sources of random variation?

Heights of Adult Males Narrative The distribution of heights of adult males has a mean of 175.0 cm and a standard deviation of 10.0 cm. A random sample of 36 adult males is selected. -Refer to Heights of Adult Males Narrative. Find the probability that the average height will be more than 177.5 cm.