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Fund Statistics Assignment # 4

Variability

Instructions: Show your work to get credit. Use the online text submission link or prepare your responses as a word doc, then attached for submission.

1. Explain or define variance and standard deviation and describe how they are related.

2. For the sample of scores: 2, 4, 6, 7, 8, 9, compute (a) the range, (b) interquartile range (c) deviation scores, (d) the sample variance, (e) the sample standard deviation.

3. The variance calculated on a sample of 25 cases is 4. What is the sum of the squared deviations (SS)?

4. The standard deviation for a population of scores is 15, with SS = 5625, how many scores were in the population?

5. The standard deviation for a sample of scores is 10. What will the standard deviation be if each score is (a) multiplied by a constant of 5, (b) divided by a constant of 5, and (c) adding a constant of 5 to each score?

6.  For the sample of scores: 3, 4, 6, 7, (a) show that the sum of the deviation scores is 0, (b) using the definitional formula, compute the sum of the squared deviations (SS), (c) using the computational formula, compute SS, (d) state when to use the definitional and computational formulas for SS.

7. The sum of squares of a set of 25 scores is 960. What are the variance and standard deviation, assuming the set of scores came from a sample?

8. The standard deviation of a distribution of 250 scores (assuming a population) is 15. What is the variance? What is the sum of squares?

Fund Statistics

Z-Scores and Probability

Assignment # 5

1.    In a population scores are normally distributed with mean of 100, SD = 15:

a.    Find the z-score corresponding to a score of 95.

b.    If a z-score is 2, what was the raw score (X) value?

c.    What is the probability of getting a score that is greater than 95?

d.    What is the probability of obtaining a score that is less than 95?

e.    What proportion of scores fall between 95 and 105?

f.     What is the probability of obtaining a score that is greater than 110?

g.    What is the probability of getting a score that is between 105 and 110?

h.    What score is needed to be in the top 15% of the distribution?

i.      What score is needed to be in the top 70% of the distribution?

j.      If a score (X) = 75 in the original distribution with M = 100, SD = 15, what will be the new score if the original distribution is now standardized with M = 500 and SD = 100.

2.    In a multiple choice exam consisting of 48 questions, with four possible answers for each question, (a) what is the probability of getting more than 15 correct just by guessing? (b) what is the probability of getting at least 15 correct just by guessing? (c) what is the probability of getting exactly 15 correct just by guessing?

3.    a. Suppose that in a population of IQ scores, only 1% of the scores are below 70 and 2% are above 130. If we select one member of the population at random, what is the probability of an IQ score less than 70 or greater than 130.

b. If we randomly and independently select three children from a population in which p (IQ > 130) = .02, what is the probability that all three children have IQ > 130?

4.    Define the distribution of sample means. List and describe the characteristics of the distribution of sample means.

For a normally distributed population with µ= 60 and σ = 12. (a) How much error would you expect between the sample mean and the population mean? (Hint: calculate standard error), (b) what is the probability of selecting a random sample on n = 36 scores with a sample mean greater than 64?

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