2. The power draw for two different types of microchips are being compared. It i

Question

2. The power draw for two different types of microchips are being compared. It is known that the standard deviation of both microchips are approximately equal (o-1.5 mW). Two random samples of microchips are tested with ni-20, 1 = 21 mW, n2=25, 22 mW. (10 pts) (a) Test the hypothesis that both microchips have the same power draw. Use =0.05. (b) What is the p-value of this test? (c) Construct a 95% confidence interval for the difference in population means 1-12. (d) What is the type II error probability if the true difference in means is as large as 0.75 mw? (e) What equal sample size would be needed to have a power of 90% when detecting a true difference in means as large as 0.75 mW? 3. Repeat question 2 but do not assume that we know . Use sample standard deviations s1= 1.35 mw and s2= 1.55 mW. (10 pts)

Explanation / Answer

p-value = 0.0257

As p-value is less than the significance level of 0.05, we reject the null hypothesis.

this means there are significant evidence to conclude that there is difference in means.

Confidence interval

Type II error

hypothesised mean = 0

True mean = 0.75

z-critical = +/- 1.96

x-critical = +/- 0.85

Beta or type II error is the probability of fail to reject the null hypothesis

Hence type II error probability is 0.4105

Null Hypothesis Alternate Hypothesis H0: 1 - 2 = 0 Ha: 1 - 2 0

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