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Exam 4: Variability.

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Question 1

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A researcher takes a sample from a population and computes a statistic for the sample.Which of the following statements is correct?

A) If the sample statistic overestimates the corresponding population parameter, then the statistic is biased.
B) If the sample statistic underestimates the corresponding population parameter, then the statistic is biased.
C) If the sample statistic is equal to the corresponding population parameter, then the statistic is unbiased.
D) None of the other statements is correct.

E) None of the above
F) C) and D)

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Question 2

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Which of the following actions will have no effect on the value of the standard deviation?

A) Multiply each score in the distribution by 2
B) Divide each score in the distribution by 2
C) Subtract 5 points from every score in the distribution
D) All of the other actions will change the value of the standard deviation

E) None of the above
F) A) and B)

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Question 3

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A sample with SS = 40 and a variance of 8 has n = 5 scores.

The sum of the squared deviation scores is SS = 20 for a sample of n = 5 scores.What is the variance for this sample?

Without some correction,sample variability is said to be "biased." Define the term biased,and explain how this bias is corrected in the formula for sample variance.

A population of N = 100 scores has µ = 30 and σ = 4.What is the population variance?

Calculate the variance and the standard deviation for the following sample data.Scores: 1,0,3,1,2,4,0,1

Multiplying every score in a sample by 3 will not change the value of the standard deviation.

A sample of n = 9 scores has a variance of s² = 18.If the scores were a population,what value would be obtained for the population variance?

For the following sample,use the computational formula to calculate SS and then compute the sample variance and standard deviation.Scores: 1,3,1,1

All the possible samples of n = 3 scores are selected from a population with µ = 30 and Ϭ = 5 and the mean is computed for each of the samples.If the average is calculated for all of the sample means,what value will be obtained?

One sample is selected to represent scores in treatment 1 and a second sample is used to represent scores in treatment 2.Which set of sample statistics would present the clearest picture of a real difference between the two treatments?

Which of the following symbols identifies the population standard deviation?

What is the value of SS for the following set of scores? Scores: 1,1,4,0

What is the value of SS (sum of squared deviations) for the following sample? Sample: 1,1,1,7

If the highest score in a distribution is X = 16 and the lowest is X = 4,then the range is 12 or 13 points.

A sample of n = 7 scores has SS = 42.The variance for this sample is s² = 6.

It is easier to see the mean difference between two samples if the sample variances are small.

There is a 6-point difference between two sample means.If the two samples have the same variance,which of the following values would make the mean difference easiest to see in a graph showing the two distributions?

A set of scores ranges from a high of X = 34 to a low of X = 24 and has a mean of 29.Which of the following is the most likely value for the standard deviation for these scores?