Exam 8: Sampling Distributions

In the upcoming election for governor, the most recent poll, based on 900 respondents, predicts that the incumbent will be reelected with 55 percent of the votes. For the sake of argument, assume that 51 percent of the actual voters in the state support the incumbent governor (p = .51). Calculate the probability of observing a sample proportion of voters .55 or higher supporting the incumbent governor.

If a population distribution is known to be normal, then it follows that

As the sample size increases, the standard deviation of the sampling distribution increases.

If the sampled population distribution is skewed then, in most cases, the sampling distribution of the mean can be approximated by the normal distribution if the sample size, n, is at least 30.

A random sample of size 36 is taken from a population with mean 50 and standard deviation 5. Find P( < 51.5).

Whenever the population has a normal distribution, the sampling distribution of is a normal, or near normal, distribution

The Central Limit Theorem states that as the sample size increases, the distribution of the sample ________ approaches the normal distribution.

Find P( > 2,510) if μ = 2,500 and = 7.

If we have a sample size of 100 and the estimate of the population proportion is .10, we can estimate the sampling distribution of with a normal distribution.

The sampling distribution of must be a normal distribution with mean = 0 and standard deviation = 1.

The diameter of small Nerf balls manufactured overseas is expected to be approximately normally distributed with a mean of 5.2 inches and a standard deviation of .08 inches. Suppose a random sample of 20 balls is selected. What percentage of sample means will be less than 5.14 inches?

A minimum-variance unbiased point estimate has a variance that is as small as or smaller than the variances of any other unbiased point estimate.

The sampling distribution of the sample mean is a normal distribution for ________ sample sizes, regardless of the shape of the corresponding population distribution.

An unbiased estimate of σ² is ________.

A manufacturing company measures the weight of boxes before shipping them to the customers. If the box weights have a population mean and standard deviation of 90 lb and 24 lb, respectively, then based on a sample size of 36 boxes, what is the probability that the average weight of the boxes will exceed 94 lb?

Find P( < 402), if μ = 400, σ = 200, and n = 100.

If p = .9 and n = 40, then we can conclude that the sampling distribution of is approximately a normal distribution.

It has been reported that the average time to download the home page from a government website was .9 seconds. Suppose that the download times were normally distributed with a standard deviation of .3 seconds. If random samples of 36 download times are selected, what is the probability that the sample mean will be less than .84 seconds?

The population of lengths of aluminum-coated steel sheets is normally distributed with a mean of 30.05 inches and a standard deviation of .2 inches. What is the probability that a randomly selected sample of 4 sheets will have an average length of less than 29.9 inches long?

For nonnormal populations, as the sample size (n) ________, the distribution of sample means approaches a(n) ________ distribution.