Given the following hypothesis: H_0: mu = 100 H_1. mu notequalto 100 A random sa

Question

Given the following hypothesis: H_0: mu = 100 H_1. mu notequalto 100 A random sample of six resulted in the following values: 102 110 116 111 113 114 Using the 0.02 significance level, can wo conclude that the mean is different from 100? What is the decision rule? (Negative answer should be indicated by minus sign. Round the final answers to 3 decimal places.) Reject H_0: mu = 100 and accept H_1: mu notequalto 100 when the tot's statistic is Compute the value of the test statistic (Round the final answer to decimal places.) Value of the test statistic What is your decision regarding H_0? Estimate the p-value Use the results of the confidence interval to support your decision in part (c)

Explanation / Answer

a) alph = 0.02

n = 6 ,

t0.01,5 = 3.365

so when test statistic is outside ( - 3.365 , 3.365) ,we reject the null hypothesis

b) mean = 111 , sd = 4.89898

test statistic = (111-100)/(4.89898/sqrt(6)) = 5.4999

c) since 5.4999 > 3.365

we reject the null hypothesis

d) p-value = 2*(1-0.9986) = 0.0028

e) confidence interval = (111 - 3.365 * 4.8989 / sqrt(6) , 111 + 3.365 * 4.8989 / sqrt(6))

= (104.270, 117.729)

f) since 100 is not in confidence interval, we reject the null hypothesis

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