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Chapter 4: Q124E (page 270)

Ranking PhD programs in economics. Refer to the SouthernEconomic Journal(April 2008) rankings of PhD programsin economics at 129 colleges and universities, Exercise 2.103(p. 117). Recall that the number of publications published byfaculty teaching in the PhD program and the quality of thepublications were used to calculate an overall productivityscore for each program. The mean and standard deviationof these 129 productivity scores were then used to computea z-score for each economics program. The data (z-scores)for all 129 economic programs are saved in the accompanying

file. A Minitab normal probability plot for the z-scores isshown below. Use the graph to assess whether the data areapproximately normal.

Short Answer

Expert verified

The quantile- quantile line and data points are not falling approximately one upon another. So, the data score is not normally distributed.

Step by step solution

01

Given information

The graph of the 129 productivity scores is given,

02

Explanation

From the above graph, it is shown that the data points do not fall in a straight line.

The maximum data points fall below the quantile-quantile line. The lower and upper portions of the data points fall below the line, and only the middle portion of the data points fall on the line.

So, it can be concluded that the productivity score is not approximately normally distributed.

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Most popular questions from this chapter

Purchasing decision. Suppose you are a purchasing officer for a large company. You have purchased 5 million electrical switches, and your supplier has guaranteed that the shipment will contain no more than .1% defectives. To check the shipment, you randomly sample 500 switches, test them, and find that four are defective. Based on this evidence, do you think the supplier has complied with the guarantee? Explain

178 Dutch elm disease. A nursery advertises that it has 10 elm treesfor sale. Unknown to the nursery, 3 of the trees have already been infected with Dutch elm disease and will die withina year.

a. If a buyer purchases 2 trees, what is the probability that bothtrees will be healthy?

b. Refer to part a. What is the probability that at least 1 of thetrees is infected?

Suppose x is a binomial random variable with p = .4 and n = 25.

a. Would it be appropriate to approximate the probability distribution of x with a normal distribution? Explain.

b. Assuming that a normal distribution provides an adequate approximation to the distribution of x, what are the mean and variance of the approximating normal distribution?

c. Use Table I in Appendix D to find the exact value of P(x≥9).

d. Use the normal approximation to find P(x≥9).

Find az-score, call itz0, such that

a.P(z≤z0)=.5080

b.P(z≥z0)=.5517

c.P(z≥z0)=.1492

d.P(z0≤z≤.59)=.4773

If x is a binomial random variable, compute for each of the following cases:

  1. n = 4, x = 2, p = .2
  2. n = 3, x = 0, p = .7
  3. n = 5, x = 3, p = .1
  4. n = 3, x = 1, p = .9
  5. n = 3, x = 1, p = .3
  6. n = 4, x = 2, p = .6
See all solutions

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