Question

Server response time is an important quality characteristic (CTQ). As an engineer you are interested to check whether the response time is significantly different/higher/lower from 100 milliseconds for given cases below. If the test statistics (Z0) is known, find the P-values for the following alternative hypotheses (μ ≠ 100, μ > 100, μ < 100)

NOTE: PLEASE COMPLETE THIS TASK USING MICROSOFT WORD OR SOME OTHER DIGITAL CONTENT EDITOR.

H₀: μ = 100

H₁: μ ≠ 100.

(a) Z0 = 1.86

(b) Z0 = −2.05

___________________

H₀: μ = 100

H₁: μ > 100.

(c) Z0 = 2.50

(d) Z0 = −1.95

___________________

H₀: μ = 100

H₁: μ < 100.

(e) Z0 = −2.35

(f) Z0 = −1.99

Answer 1

H0: μ = 100

H1: μ ≠ 100.

(a) Z0 = 1.86

p-value = 2 * P(Z > 1.86) = 2 * 0.0314 = 0.0628

=> p-value = 0.0628

(b) Z0 = −2.05

p-value = 2 * P(Z < -2.05) = 2 * 0.0202 = 0.0404

=> p-value = 0.0404

H0: μ = 100

H1: μ > 100.

(c) Z0 = 2.50

p-value = P(Z > 2.50) = 0.0062

=> p-value = 0.0062

(d) Z0 = −1.95

p-value = P(Z > -1.95) = 0.9745

=> p-value = 0.9744

H0: μ = 100

H1: μ < 100.

(e) Z0 = −2.35

p-value = P(Z < -2.35) = 0.0094

=> p-value = 0.0094

(f) Z0 = −1.99

p-value = P(Z < -1.99) = 0.0233

=> p-value = 0.0233