For Exercise 1.70, see page 40; for 1.71 to 1.73, see pages 41-42; for 1.74 to 1.77, see pages 44-45; for 1.78, see page 46; for 1.79 and 1.80, see page 49; for 1.81 and 1.82, see page 50; and for 1.83 and 1.84, see page 53.

Question 1.83

1.83 Length of time to start a business.

CASE 1.2 In Exercise 1.33, we noted that the sample of times to start a business from 25 countries contained an outlier. For Suriname, the reported time is 208 days. This case is the most extreme in the entire data set. Figure 1.30 shows the Normal quantile plot for all 189 countries, including Suriname.

  1. These data are skewed to the right. How does this feature appear in the Normal quantile plot?
  2. Find the point for Suriname on the plot. Do you think that Suriname is truly an outlier, or is it part of a very long tail in this distribution? Explain your answer.
  3. Compare the shape of the upper portion of this Normal quantile plot with the upper portion of the plot for the T-bill interest rates in Figure 1.29, and with the upper portion of the plot for the IQ scores in Figure 1.28. Make a general statement about what the shape of the upper portion of a Normal quantile plot tells you about the upper tail of a distribution.

1.83

(a) The points fall below the 45º line; they form a straight line at first but then, near the right side, begin to increase steeply, indicating the right-skew. (b) It is likely part of a very long tail as it aligns perfectly with the curvature; see the Normal quantile plot. (c) The upper portion of the Normal quantile plot can show if a right-skew exists; specifically, if the points on the plot get steeper than a 45º line, this indicates a right-skew or long right tail.

tts25