Exam 7: Sampling Distributions

According to the Central Limit Theorem, if is the mean of a simple random sample taken from a large population, and if the N population values are not normally distributed, the sampling distribution of nevertheless approaches a normal distribution as sample size, n, increases.

Examination Times Narrative The time necessary to complete an examination has a mean of 45 minutes and a standard deviation of 4 minutes. The average time necessary for 64 randomly selected students is computed. -Refer to Examination Times Narrative. Completely describe the sampling distribution of the sample mean.

Suppose that 20% of the households in Alberta have incomes in excess of $60,000. Assume that a random sample of 500 households in Alberta is taken. What will be the standard error of the sampling distribution of sample proportion of households that have incomes in excess of $60,000?

A systematic random sample has the advantage of being usable for a population that may be ordered in some way but whose size we may not know at any given time.

What is the term for a numerical descriptive measure calculated from the entire population?

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

If a population standard deviation is equal to 24.8, then the sampling distribution of the sample mean, , will have a standard deviation that is less than 24.8 for all possible sample sizes.

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.

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. What was the sample size, n?

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. Find the probability that the sample proportion "on" will be between 0.65 and 0.75.

When all possible simple random samples of size n are drawn from a population that is normally distributed, the sampling distribution of the sample means will be normal, regardless of sample size, n.

The latest census shows the population aged 25 to 40 to be 48% male and 52% female. A market research firm interested in the buying habits of young adults aged 25 to 40 instructs its interviewers to sample 300 persons, 144 of whom are to be men and 156 of whom are to be women. This is an example of a quota sample.

A summary measure calculated for a population is called a parameter and is designated by Greek letters (such as for mean or for proportion).

Suppose that 56% of all registered voters in Ontario are supporting a certain candidate for prime minister A sample of 1500 voters is selected at random from Ontario. Based on the concept of sampling distribution of sample proportion, , it can be assumed that = 0.56.

Content Composition Analysis Narrative 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. -Refer to Content Composition Analysis Narrative. Would a value of = 0.25 be considered unusual? Justify your answer.

Weights of Chocolate Bars Narrative A candy bar factory is pouring chocolate into moulds to cool. The finished bars are sold as 35 gram bars. The company will lose money if the moulds are overfilled. If the moulds are underfilled, the weight of the candy bars will be less than the wrapper label says, and the company will be subject to a fine for misrepresenting the size of its product. The company wants to create an chart to monitor the weight of the candy bars. Suppose 5 samples are taken, each of size 30, having the sample means 36.1, 34.6, 35.8, 34.9, and 35.8 grams, respectively. -Refer to Weights of Chocolate Bars Narrative. What are the control limits?

Miller Analogies Test Narrative Graduate students applying for entrance to many universities must take a Miller Analogies Test. It is known that the test scores have a mean of 75 and a variance of 16. In 1990, 100 students applied for entrance into graduate school in physics. -Refer to Miller Analogies Test Narrative. Find the probability that the average score of this group of students is higher than 76.

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. What is the probability that the sample proportion is less than 0.10?

Federal Budget Narrative Suppose public opinion is split 65% against and 35% for increasing taxes to help balance the federal budget. Suppose also that 500 people from the population are selected randomly and interviewed. -Refer to Federal Budget Narrative. Completely describe the sampling distribution of the sample proportion of people who are in favour of increasing taxes to help balance the federal budget.

Rh-Positive Blood Type Narrative The proportion of individuals with an Rh-positive blood type is 88%. You have a random sample of n = 500 individuals. -Refer to Rh-Positive Blood Type Narrative. What is the probability that the sample proportion exceeds 85%?