Test the indicated claim about the means of two popualtions. Assume that the two

Question

Test the indicated claim about the means of two popualtions. Assume that the two samples are independent simple random samples selected from normally distributed populations. Do not assume that the population standard deviations are equal. Use the Critical Value method or P-Value method as indicated.

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Two types of flares are tested for their burning times (in minutes) and sample resutls are given below

Brand X Brand Y

n = 35 n = 40

x1= 19.4 min x2= 15.1 min

s = 1.4 min s = .08

Use a 0.05 significance level to test the claim that the two samples are from populations with the same mean. Use the Critical Value method of hypothesis testing. State and determine the null hypothesis, alternative hypothesis, test statistic, critical values and conclusion addressing the original claim.

Use Degree of Freedom = 50

Explanation / Answer

Std Error = sqrt[(s12/n1) + (s22/n2)] = sqrt[(1.42/35) + (0.082/40)] = 0.237

Test stat t = [ (x1 - x2) ] / SE = (19.4 - 15.1)/0.237 = 18.145

Degrees of Freedom = 50

Critical value for df = 50 and significance level 0.05 is +2.01

Rejection region is test stat < critical value (-2.01) or test stat > critical value (2.01)

Since the test stat lies in the rejection region we reject the null hyp and conclude that the two samples are not from populations with the same mean

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