Given the following hypotheses: H_0: mu = 100 H_A: mu notequalto 100 Suppose tha

Question

Given the following hypotheses: H_0: mu = 100 H_A: mu notequalto 100 Suppose that a random sample of 6 is drawn from the population. The sample mean is equal to 111.67 and the sample standard deviation is equal to 6.055. (a) State the decision rule using the critical value approach. Use the alpha = 0.05 significance level. (b) State the decision rule using the p-value approach. Use the alpha = 0.05 significance level. (c) Compute the value of the test statistic (d) Find the p-value (e) Will you reject or fail to reject the null hypothesis? Explain your answer.

Explanation / Answer

a) for rejection region t>2.5706 or z<-2.5706

b)rejection region p value <0.05

c)for std error =6.055/(6)1/2 =2.4719

hence test stat t=(X-mean)/std error =(111.67-100)/2.4719 =4.7210

d) p value for above =0.0052

e) as from both criteria , t stat and p value fall into rejection area ; we reject null hypothesis

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