Question

Predicting software blights. Relate to the Pledge Software Engineering Repository data on 498 modules of software law written in “C” language for a NASA spacecraft instrument, saved in the train. (See Exercise 3.132, p. 209). Recall that the software law in each module was estimated for blights; 49 were classified as “true” (i.e., the module has imperfect law), and 449 were classified as “false” (i.e., the module has corrected law). Consider these to be Arbitrary independent samples of software law modules. Experimenters prognosticated the disfigurement status of each module using the simple algorithm, “If the number of lines of law in the module exceeds 50, prognosticate the module to have a disfigurement.” The accompanying SPSS printout shows the number of modules in each of the two samples that were prognosticated to have blights (PRED_LOC = “yes”) and prognosticated to have no blights (PRED_LOC = “no”). Now, define the delicacy rate of the algorithm as the proportion of modules. That was rightly prognosticated. Compare the delicacy rate of the algorithm when applied to modules with imperfect law with the delicacy rate of the algorithm when applied to modules with correct law. Use a 99-confidence interval.

DEFECT*PRED_LOC crosstabulation

	PRED_LOC		total
	no	yes
DEFECT False True total	440 29 429	49 20 69	449 49 498

Short answer

The difference in accuracy rate between the modules with correct code and modules with incorrect lies between 0.2948 and 0.6652 at 99% confidence.

Step-by-step solution

Step-by-Step Solution Step 1: Find the value of P1 and P2

Consider n₁=449, n₂=49, x₁ = 400, x₂=20.

Find the value of p₁.

$\begin{array}{l}{\underset{\_}{P}}_1=\frac{x_1}{n_1}\\ =\frac{400}{449}\\ =0.89\\ \\ Findthevalueof{p}_2.\\ {\underset{\_}{p}}_2=\frac{x_2}{n_2}\\ =\frac{22}{49}\\ =0.41\end{array}$

Let the confidence level be 0.99

$\begin{array}{l}1-\alpha =0.99\\ \alpha =1-0.99\\ =0.01\\ \frac{\alpha }{2}=0.005\end{array}$

From appendix table-2, the value of Za_/2 is given below.

$\begin{array}{l}{Z}_{\frac{a}{2}}=Z_{0.005}\\ =2.58\end{array}$

So, the value of $z_{\frac{a}{2}}$ is 2.58.

The formula for 100(1α) % confidence intervals for (P1-P2)

The formula for 100(1α) % confidence intervals for (P₁-P₂) is below.

$({\underset{\_}{p}}_1-\underset{\_}{p_2})\pm z_{\frac{a}{2}}\left[\sqrt{\frac{{\underset{\_}{p}}_1{\underset{\_}{q}}_1}{n_1}+\frac{p_2{q}_2}{n_2}}\right]$

In this, q₁ = 1 – p₁and q₂ = 1 – p_2.

Find the 99% confidence interval for (P1-P2)

Substitute P₁ = 0.89 P₂ = .041, n₁ = 449, and n₂ = 49 in the above formula.

= 0.89 – 0.41 ± 2.58 $\left[\sqrt{\frac{0.89(1-0.89)}{+\frac{4490.41(1-0\cdot 41)}{49}}}\right]$

=0.48±2.58role="math" localid="1652718669873" $\left(\sqrt{\frac{0.0979}{449}+\frac{0.2419}{49}}\right)$

=0.48±2.58(0.0718)

=.48±0.1852

= (0.2948,0.6652)

Thus, the 99% confidence interval for (P₁ – P₂) is (0.2948,0.6652).

Final answer

The difference in accuracy rate between the modules with correct code and modules with incorrect lies between 0.2948 and 0.6652 at 99% confidence.