Hypothesis Testing and Confidence Interval Analysis

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Hypothesis Testing and Confidence Interval AnalysisSolution:Null hypothesis H0: μ1-μ2=0 against H1: μ1-μ2≠0Since the sample size n <30 therefore the test will be t test and the test statisticst=𝑠𝑎𝑚𝑝𝑙𝑒1𝑚𝑒𝑎𝑛−𝑠𝑎𝑚𝑝𝑙𝑒2𝑚𝑒𝑎𝑛−(μ1−μ2)√(𝑠12𝑛1+𝑠22𝑛2)where s12,s22is the sample variance of the sample 1 and sample2, n1 and n2 are the sample size of those two samples.Under the null hypothesis t the results are as follows:

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a)Fail to reject the null hypothesis because the calculated t=0.49< critical t =1.72.b)Test t=0.49c)P value for the test is 0.63.d)Critical t values are +/-1.72.t-Test: Two-Sample Assuming Equal VariancesCo-opsInternsMean15.6515.44Variance1.190.92Observations12.0012.00Pooled Variance1.06Hypothesized Mean Difference0.00df22.00t Stat0.49P(T<=t) one-tail0.31t Critical one-tail1.32P(T<=t) two-tail0.63t Critical two-tail1.72

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Solution:Null hypothesis H0: μ1-μ2>0 against H1: μ1-μ2≤0Since the sample size n <30 therefore the test will be t test and the test statisticst=𝑠𝑎𝑚𝑝𝑙𝑒1𝑚𝑒𝑎𝑛−𝑠𝑎𝑚𝑝𝑙𝑒2𝑚𝑒𝑎𝑛−(μ1−μ2)√(𝑠12𝑛1+𝑠22𝑛2)where s12,s22is the sample variance of the sample 1 and sample2, n1 and n2 are the sample size of those two samples.Under the null hypothesis t the results are as follows:

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