A random sample of 100 observations from a population with standard deviation 60

Question

A random sample of 100 observations from a population with standard deviation 60 yielded a sample mean of 110. a. Test the null hypothesis that mu = 100 against the alternative hypothesis that mu > 100, using alpha = .05 Interpret the results of the test. b. Test the null hypothesis that mu = 100 against the alternative hypothesis that mu notequalto100, using alpha = .05. Interpret the results of the test. c. Compare the p-values of the two tests you conducted. Explain why the results differ.

Explanation / Answer

a) std error of mean =std deviation/(n)1/2 =6

test stat z=|(X-mean)/std error =(110-100)/6=1.6667

for one tailed test p value =0.0478

as p value is less then 0.05 we reject null hypothesis and conclude that mean is greater then 100.

b) for two tailed test p value =0.0478*2=0.0956

as p value is greater then 0.05 we fail to reject null hypothesis and can not conclude that mean is different from 100.

c) as for two tailed test rejection region is in both tails therefore it has larger twice the p value for same test stat, in comparison to one tail test

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