Question

Chopter 10 Example Engineers working at a manufacturing plant realized that 15% of their product needed to be recaledn order to fix a faulty component. After making changes to the original design, they kept track of all recent orders (n 88) and found 9.5% of orders still needed to be fixed. However, could the changes made by the engineers, be considered a significant improvement? (Use an α-level of 0.10) ISA 225 Example: A 2010 article reported that out of 1109 CEOs from global companies 32% had MBAs. Could we say the percentage changed, given an older study found that only 29% of CEOs previously held MBAs? (Use α 0.05)

Answer 1

a) H₀: P = 0.15

    H₁: P < 0.15

The test statistic z = ($\widehat p$ - P)/sqrt(P(1 - P)/n)

                              = (0.095 - 0.15)/sqrt(0.15 * (1 - 0.15)/88)

                              = -1.44

P-value = P(Z < -1.44)

             = 0.0749

Since the P-value is less than the significance level(0.0749 < 0.10), so we should reject the null hypothesis.

So at 0.10 significance level we can conclude that the changes made by the engineers still be considered a significant improvement.

b) H₀: P = 0.29

    H₁: P $\dpi{100} \neq$ 0.29

The test statistic z = ($\widehat p$ - P)/sqrt(P(1 - P)/n)

                              = (0.32 - 0.29)/sqrt(0.29 * (1 - 0.29)/1109)

                              = 2.20

P-value = 2 * P(Z > 2.20)

              = 2 * (1 - P(Z < 2.20))

              = 2 * (1 - 0.9861)

              = 2 * 0.0139

              = 0.0278

Since the P-value is less than the significance level(0.0278 < 0.05), so we should reject the null hypothesis.

So at 5% significance level there is sufficient evidence to conclude that the percentage of CEOs held MBAs has been changed..