A manufacturing produces automobiles in two different systems (system A and syst

Question

A manufacturing produces automobiles in two different systems (system A and system B). However, an engineer observed that system A produces defective cars higher than system B. To support this theory, 100 cars built in system A is selected, 8 of them were defects. A random sample of 200 cars built in system B. 12 of them were defects. Let: P_a = proportion of defective cars from system A P_b = proportion of defective cars from system B Construct a 90% confidence interval for the difference in the proportions of defective cars from system A and system B. Test the hypothesis whether the proportion of defective cars from system A is higher than proportion of defective cars from system B at alpha = 0.05. Using the same hypothesis, test the hypothesis at alpha = 0.35. Is there any difference in your conclusion in (ii) and (iii)? If yes, explain. Babies To Go Sdn. Bhd ¡s the manufacturer of car seats for children. They manufacture two distinct types of car seats. They want to test the car seats for durability. The results of the test are given in the following table. The mean and standard deviation of durability is in months (Assume the two population variances are not equal). Construct a 95% confidence interval for the mean difference in car seats durability. Can we conclude that the mean difference in car seats durability is more than 3.4 months at alpha = 0.01?

Explanation / Answer

Solution :-

d = 1 - 2 = 11.4 - 7.5 = 3.9

d = sqrt( 12 / n1 + 22 / n2 )
d = sqrt((1.2)2/15 + (0.8)2/10) = sqrt(1.44/15 + 0.64/10) = sqrt(0.096 + 0.064) = sqrt(0.16) = 0.4

z = (x - )/ = (3.4 - 3.9)/0.4 = -0.5/0.4 = -1.25

Specifically, we enter the following inputs: -1.25, for the normal random variable; 0, for the mean; and 1, for the standard deviation.

We find that the probability of probability of a z-score being -1.818 or less is about 0.10565.

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