Question 7.5: Industrial firms often employ methods of "risk transfer," su...
Industrial firms often employ methods of “risk transfer,” such as insurance or indemnity clauses in contracts, as a technique of risk management. The article “Survey of Risk Management in Major U.K. Companies” (S. Baker, K. Ponniah, and S. Smith, Journal of Professional Issues in Engineering Education and Practice, 1999:94- 102) reports the results of a survey in which managers were asked which methods played a major role in the risk management strategy of their firms. In a sample of 43 oil companies, 22 indicated that risk transfer played a major role, while in a sample of 93 construction companies, 55 reported that risk transfer played a major role. (These figures were read from a graph.) Can we conclude that the proportion of oil companies that employ the method of risk transfer is less than the proportion of construction companies that do?
Let \hat{p}_X=22 / 43=0.5116 be the sample proportion of oil companies employing risk transfer methods, and let \hat{p}_Y=55 / 93=0.5914 be the corresponding sample proportion of industrial firms. The sample sizes are n_X = 43 and n_Y = 93. Let p_X and p_Y denote the population prop0rtions for oil and industrial companies, respectively. The null and alternate hypotheses are
H_0: p_X-p_Y \geq 0\,\, \text{versus}\,\,H_1: p_X-p_Y<0
The pooled proportion is
\hat{p}=\frac{22+55}{43+93}=0.5662
The null distribution is normal with mean 0 and standard deviation
\sqrt{0.5662(1-0.5662)(1 /43 + 1/93)}=0.0914
The observed value of \hat{p}_X-\hat{p}_Y \,\,\text{is}\,\,0.5116-0.5914=-0.0798. The z-score is
z=\frac{-0.0798-0}{0.0914}=-0.87
The P-value is 0.1922 (see Figure 7.3). We cannot conclude that the proportion of oil companies employing risk transfer methods is less than the proportion of industrial firms that do.
