Exam 8: Sampling Distributions

Barack Obama Bill Clinton, the former President of the United States, believes that the proportion of voters who will vote for Barack Obama in the year 2012 presidential elections is 0.65. A sample of 500 voters is selected at random. -{Barack Obama Narrative} Assume that Gore is correct and p = 0.65. What is the sampling distribution of the sample proportion ? Explain.

The Central Limit Theorem states that, if a random sample of size n is drawn from a population, then the sampling distribution of the sample mean :

The normal approximation to the binomial distribution gets better and better as ____________________ increases.

Consider an infinite population with a mean of 160 and a standard deviation of 25. A random sample of size 64 is taken from this population. The standard deviation of the sample mean equals:

Retirees: A sample of 50 retirees is drawn at random from a normal population whose mean age and standard deviation are 75 and 6 years, respectively. -What is the probability that the mean age exceeds 73 years?

Average Annual Revenue Suppose that the average annual revenue of a small business is $150,000 with a standard deviation of $40,000. Assume that the revenue distribution is normal. -{Average Annual Revenue Narrative} Could you have used a normal distribution to find an (approximate) probability for the average of 4 revenues if the population of revenues did not have a normal distribution?

DVD Rental Store A DVD rental store wants to know what proportion of its customers are under age 21. A simple random sample of 500 customers was taken, and 375 of them were under age 21. Presume that the true population proportion of customers under age 21 is 0.68. -{DVD Rental Store Narrative} Find the mean and standard deviation of .

A sample of size 25 is selected from a population of size 500. The finite population correction is needed to find the standard error of .

Suppose that 100 items are drawn from a population of manufactured products and the weight, X, of each item is recorded. Prior experience has shown that the weight has a non-normal probability distribution with $\mu$ = 8 ounces and $\sigma$ = 3 ounces. Which of the following is true about the sampling of ?

Consider an infinite population with a mean of 100 and a standard deviation of 20. A random sample of size 64 is taken from this population. The standard deviation of the sample mean equals 2.50.

If a random sample of size n is drawn from a normal population, then the sampling distribution of the sample mean will be:

As a general rule, the normal distribution is used to approximate the sampling distribution of the sample proportion only if:

For a sample size of 1, the sampling distribution of the mean is normally distributed:

The standard error of the mean:

As n gets larger, the sampling distribution of becomes increasingly bell shaped. This phenomenon is due to the ____________________.

Under certain conditions where n is large enough, you can approximate the ____________________ distribution using the ____________________ distribution.

Given an infinite population with a mean of 75 and a standard deviation of 12, the probability that the mean of a sample of 36 observations, taken at random from this population, is less than 78 is:

Poker Time: The amount of time spent by American adults playing Poker per week is normally distributed with a mean of 4 hours and standard deviation of 1.25 hours. -Find the probability that a randomly selected American adult plays Poker for more than 5 hours per week.

Barack Obama Bill Clinton, the former President of the United States, believes that the proportion of voters who will vote for Barack Obama in the year 2012 presidential elections is 0.65. A sample of 500 voters is selected at random. -{Barack Obama Narrative} Find the expected value and the standard deviation of the sample proportion .

Graduate Internships The chairman of the Biology department in a certain college believes that 70% of the department's graduate internships are given to international students. A random sample of 50 graduate interns is taken. -{Graduate Internships Narrative} Assume that the chairman is correct and p = 0.70. What is the sampling distribution of the sample proportion ? Explain.