Exam 15: Sample Size and Statistical Theory

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Use the following information for questions A soap factory produces 500-pound boxes of soap for industries. However, the weight of the boxes varies somewhat due to the process. Assume that the weight of each box is distributed normally with mean = μ\mu = 500 pounds variance = σ\sigma 2 = 25 pounds2 Quality control takes a random sample of 25 boxes per day.Let the weight of these boxes be denoted as X1, X2, ..., X25. -The probability that the sample mean lies between 498 and 502 is closest to

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A college dean wants to determine the average time it takes a student to get from one class to the next.Preliminary studies have shown that it is reasonable to let σ\sigma t = 1.5 minutes the standard deviation of class travel times).What is the sample size which should be examined if the dean wants to assert with a probability of 95 percent that his estimate, the mean time of the random sample, will not be "off" by more than .25 minutes in either direction)? Choose the closest answer.

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If we wanted to be 95 percent confident that we wouldn't make an error of more than 1 unit in our estimate of μ\mu or σ\sigma = 2), we would need a sample size of approximately 16.

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Use the following information for questions Consider a meat packing plant which produces packages of frozen steak.Let X be the weight ounces) and assume that X is normally distributed with μ\mu x = 8.0 and σ\sigma x = .5, n sample size.= 16. -The standard error of the sample mean is

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The arithmetic average is the measurement of the sample mean.

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When a complex multi-stage design is involved, a common approach is to replicate the entire sampling plan and get various independent estimates of the sample mean.

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Consider the following: Consider the following:   For the given data: For the given data:

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It is estimated that the proportion of Californians in favor of Proposition 5 is between 0.4 and 0.6.The sponsors of the proposition would like to sample Californians and get a 95 percent confidence interval for the true proportion of people in favor of Proposition 5.They want to restrict the error level to 5 percentage points.The required sample size is then

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Bo Derek calculates that she needs a sample size of 200, given the estimated mean, accuracy variance nd required Z-score.However, she learns that the variance is actually one-half of what she originally believed.Her required sample size will now be

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Let the variance of a normally distributed random sample be 16.A point that is 8 units away from the mean is 1-a point such that the probability of getting any other point further from the mean is less than 0.025. 2-a point such that the probability of getting any other point further from the mean is less than or equal to .95. 3-a point such that the probability of getting any other point further from the mean is greater than 0.025. 4-two standard deviations away from the mean.

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The probability that a confidence level will include a population parameter is called

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A researcher takes a modest sample and, if results are worthwhile, opts for a larger sample.This type of sampling is called sequential sampling.

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A market research firm has been engaged to do a study of dishwashing detergents preferred by homemakers in San Francisco 800,000 population) as compared to those preferred in New York 8,000,000 population).In order to obtain results of about equal reliability in each city, the number of homemakers polled in New York should be

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The two population characteristics of most interest to researchers are μ\mu and σ\sigma .

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ABC Incorporated wants to find out the proportion of customers who would purchase their new product.They have decided to take a modest sample, look at the results, and then decide if more information, in the form of a larger sample, is needed.ABC is using

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Which of the following isare.a statistics)?

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What determines the statistical operations that can be performed on a scale type?

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Assume that μ\mu is distributed normally with μ\mu = 0, σ\sigma 2 = 1.What is Pz = 1)?

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If all members of the population have identical opinions on an issue, a sample of one is unsatisfactory.

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The distribution which we say always assume to be "normal " or bell shaped is the

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