Problem 3 (20%) A sample of 8 room air conditioners of model A had a mean sound

Question

Problem 3 (20%) A sample of 8 room air conditioners of model A had a mean sound pressure of 52 decibels (dB) and a standard deviation of S dB, and a sample of 12 air conditioners of model B had a mean sound pressure of 46 dB and the standard deviation of 2 d8. Assume that both samples come from approximately normal populations. Assume the population variances are equal. Find a 98% confidence interval for the difference in mean sound pressure between the two models a) b) Explain what the confidence interval you obtained in part (a) tells you d) Test the hypothesis that the population A has a higher mean sound pressure than that of population B

Explanation / Answer

Solution

(a) 98% confidence interval : ((52-46)+-2.552(48.4218(1/8 + 1/12)0.5)

sp = ((7*522+11*462)/18)0.5 = 48.4218

98% CI = (-50.4028,62.4028)

(b) The confidence interval contains 0 so there is no difference between mean of 2 samples

(c) t test = (52-46)/ 48.4218(1/8+1/12)0.5 = 0.05656

Do not reject the null hypothesis

population A mean is equal to population B mean

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