Exam 7: Sampling and Sampling Distributions

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

Suppose that 60 percent of the voters in a particular region support a candidate.Find the probability that a sample of 1,000 voters would yield a sample proportion in favor of the candidate within 2 percentage points.

Packages of sugar bags for Sweeter Sugar Inc.have an average weight of 16 ounces and a standard deviation of 0.3 ounces.The weights of the sugar bags are normally distributed.What is the probability that 9 randomly selected packages will have a weight in excess of 16.025 ounces?

The standard deviation of all possible sample proportions increases as the sample size increases.

A theorem that allows us to use the normal probability distribution to approximate the sampling distribution of sample means and sample proportions whenever the sample size is large is known as the _______________.

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

It has been reported that the average time to download the home page from a government website was 0.9 seconds.Suppose that the download times were normally distributed with a standard deviation of 0.3 seconds.If random samples of 36 download times are selected calculate the standard deviation of the sampling distribution of the sample mean.

It has been reported that the average time to download the home page from a government website was 0.9 seconds.Suppose that the download times were normally distributed with a standard deviation of 0.3 seconds.If random samples of 36 download times are selected,what is the probability that the sample mean will be less than 0.84 seconds?

The diameter of small Nerf balls manufactured at a factory in China 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?

According to a hospital administrator,historical records over the past 10 years have shown that 20% of the major surgery patients are dissatisfied with after-surgery care in the hospital.A scientific poll based on 400 hospital patients has just been conducted. What is the probability that less than 64 patients will not be satisfied with the after-surgery care?

A common practice in selecting a sample from a large geographic area is multi-stage cluster sampling.

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.

The central limit theorem states that as the sample size increases the distribution of the sample ________ approach the normal distribution.

The chief chemist for a major oil/gasoline production company claims that the regular unleaded gasoline produced by the company contains on average 4 ounces of a certain ingredient.The chemist further states that the distribution of this ingredient per gallon of regular unleaded gasoline is normal and has a standard deviation of 1.2 ounces.What is the probability of finding an average less than 3.85 ounces of this ingredient from randomly inspected 64 gallons of regular unleaded gasoline?

Find

If the sampled population has a mean 48 and standard deviation 16,then the mean and the standard deviation for the sampling distribution of for n = 16 are:

The notation for the standard deviation of the sampling distribution of the sample mean is __________.

The College Student Journal (December 1992)investigated differences in traditional and nontraditional students,where nontraditional students are defined as 25 years or older and working.Based on the study results,we can assume the population mean and standard deviation for the GPA of nontraditional students is µ = 3.5 and $\sigma$ = 0.5.Suppose a random sample of 100 nontraditional students is selected and each student's GPA is calculated.What is the probability that the random sample of 100 nontraditional students have a mean GPA greater than 3.42?

In the upcoming governor's election,the most recent poll based on 900 respondents predicts that the incumbent will be reelected with 55% of the votes.From the 900 respondents,how many indicated that they would not vote for the current governor or indicated that they were undecided?

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