2. An engineering research team is comparing two different models of motion sens

Question

2. An engineering research team is comparing two different models of motion sensor to be used for an alarm system. The team tested 360 samples of Model A and 420 samples of Model B, and found 332 Model A and 378 Model B passed the test. Conduct a test at 1% significance level to decide whether or not the team can claim that Model A is better than Model B for motion sensing a. What are the hypotheses (Ho vs. H1) for the test? b. Determine the critical value for the test c. Compute the statistic for the test d. What is the result of the test? e. Make a statement based on the result of test

Explanation / Answer

a)

H0 : P1 = P2

H1 : P1 > P2

b) Z critical value = 2.326 at 1% right tailed

Decision rule : if Z statistic > 2.326, then reject H0

c) Test statistic

= p1 - p2 / p1q1/n1 + p2q2/n2

= 0.922 - 0.9 / 0.922*1-0.922/360 + 0.9*1-0.9/420

= 1.07

d) Here Z statistic = 1.07 < 2.326, fail to reject H0

e) we conclude that there is no sufficient evidence of that model A is better than model B in motion sensing

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