Chapter 5: Q15E (page 314)
Will the sampling distribution of always be approximately normally distributed? Explain
Answer
A sampling distribution is statistics derived by continuous sampling from a greater populace.
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Refer to Exercise 5.3. Assume that a random sample of n = 2 measurements is randomly selected from the population.
a. List the different values that the sample median m may assume and find the probability of each. Then give the sampling distribution of the sample median.
b. Construct a probability histogram for the sampling distribution of the sample median and compare it with the probability histogram for the sample mean (Exercise 5.3, part b).
Question:Fingerprint expertise. Refer to the Psychological Science (August 2011) study of fingerprint identification, Exercise 4.53 (p. 239). Recall that when presented with prints from the same individual, a fingerprint expert will correctly identify the match 92% of the time. Consider a forensic database of 1,000 different pairs of fingerprints, where each pair is a match.
a. What proportion of the 1,000 pairs would you expect an expert to correctly identify as a match?
b. What is the probability that an expert will correctly identify fewer than 900 of the fingerprint matches?
Variable life insurance return rates. Refer to the International Journal of Statistical Distributions (Vol. 1, 2015) study of a variable life insurance policy, Exercise 4.97 (p. 262). Recall that a ratio (x) of the rates of return on the investment for two consecutive years was shown to have a normal distribution, with , . Consider a random sample of 100 variable life insurance policies and letrepresent the mean ratio for the sample.
a. Find E(x) and interpret its value.
b. Find Var(x).
c. Describe the shape of the sampling distribution of.
d. Find the z-score for the value .
e. Find
f. Would your answers to parts a–e change if the rates (x) of return on the investment for two consecutive years was not normally distributed? Explain.
:A random sample of n = 68 observations is selected from a population withand Approximate each of the following probabilities
a)
b)
c)
d)
Study of why EMS workers leave the job. A study of fulltimeemergency medical service (EMS) workers publishedin the Journal of Allied Health(Fall 2011) found that onlyabout 3% leave their job in order to retire. (See Exercise3.45, p. 182.) Assume that the true proportion of all fulltime
EMS workers who leave their job in order to retire is p= .03. In a random sample of 1,000 full-time EMS workers, let represent the proportion who leave their job inorder to retire.
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