Exam 8: Sampling Methods and the Central Limit Theorem

The central limit theorem states that for a sufficiently large sample,the sampling distribution of the means of all possible samples of size n generated from the population will be approximately normally distributed with the mean of the sampling distribution equal to σ² and the variance equal to σ²/n.

The central limit theorem states that if the sample size,n,is sufficiently large,the sampling distribution of the means will be approximately normal,even when the population is skewed or uniform.

The mean of all the sample means is ________.

For the sampling distribution of sample means,standard error will decrease as sample size increases.

All possible samples of size n are selected from a population,and the mean of each sample is determined. What is the mean of the sample means?

For a given population with a normal probability distribution,the sampling distribution of is a normal probability distribution for ________.

A marketing firm is studying consumer preferences for winter fashions in four different months. From a population of women 18 to 21 years of age,a random sample of 100 women was selected in January. Another random sample of 100 women was selected in March. Another random sample of 100 women was selected in June. Another random sample of 100 women was selected in September. What is the sample size?

Suppose we select every fifth invoice in a file. What type of sampling is this?

Manufacturers were subdivided into groups by volume of sales. Those with more than $100 million in sales were classified as large; those from $50 to $100 million as medium size; and those between $25 and $50 million,and so on. Samples were then selected from each of these groups. What is this type of sampling called?

The Intelligence Quotient (IQ)test scores for adults are normally distributed with a population mean of 100 and a population standard deviation of 15. What is the probability we could select a sample of 50 adults and find that the mean of this sample is between 98 and 103?

If the sampling distribution of the sample means approximates a normal distribution,then the population must be normally distributed.

The central limit theorem allows us to use a z-statistic to compute probabilities for the sampling distribution of the sample mean.

Suppose a research firm conducted a survey to determine the mean amount steady smokers spend on cigarettes during a week. A sample of 100 steady smokers revealed that the sample mean is $20. The population standard deviation is $5. What is the probability that a sample of 100 steady smokers spend between $19 and $21?

Sampling a population is often necessary because the cost of studying all the items in the population is prohibitive.

The items or individuals of the population are arranged in a file drawer alphabetically by date received. A random starting point is selected and then every kth member of the population is selected for the sample. This sampling method is called systematic random sampling.

The Office of Student Services at a large western state university maintains information on the study habits of its full-time students. Their studies indicate that the mean amount of time undergraduate students study per week is 20 hours. The hours studied follows the normal distribution with a population standard deviation of six hours. Suppose we select a random sample of 144 current students. What is the probability that the mean of this sample is between 19.25 hours and 21.0 hours?

For a distribution of sample means constructed by sampling 5 items from a population of 15,________.

In cluster sampling,a population is divided into subgroups called clusters,and a sample is randomly selected from each cluster.

The standard error of the mean is also called the sampling error.

When testing the safety of cars using crash tests,a sample of one or two cars is used because ________.