Hypothesis Testing and Confidence Interval Analysis

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Hypothesis Testing and Confidence Interval Analysis Solution: Null hypothesis H 0 : μ 1 - μ 2 =0 against H 1 : μ 1 - μ 2 ≠ 0 Since the sample size n <30 therefore the test will be t test and the test statistics t= 𝑠𝑎𝑚𝑝𝑙𝑒 1 𝑚𝑒𝑎𝑛 − 𝑠𝑎𝑚𝑝𝑙𝑒 2 𝑚𝑒𝑎𝑛 − ( μ 1 − μ 2 ) √ ( 𝑠 1 2 𝑛 1 + 𝑠 2 2 𝑛 2 ) where s1 2 ,s2 2 is the sample variance of the sample 1 and sample 2, 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=0.49 c) P value for the test is 0.63. d) Critical t values are +/ - 1.72. t-Test: Two-Sample Assuming Equal Variances Co-ops Interns Mean 15.65 15.44 Variance 1.19 0.92 Observations 12.00 12.00 Pooled Variance 1.06 Hypothesized Mean Difference 0.00 df 22.00 t Stat 0.49 P(T<=t) one-tail 0.31 t Critical one-tail 1.32 P(T<=t) two-tail 0.63 t Critical two-tail 1.72
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Solution: Null hypothesis H 0 : μ 1 - μ 2 > 0 against H 1 : μ 1 - μ 2 ≤ 0 Since the sample size n <30 therefore the test will be t test and the test statistics t= 𝑠𝑎𝑚𝑝𝑙𝑒 1 𝑚𝑒𝑎𝑛 − 𝑠𝑎𝑚𝑝𝑙𝑒 2 𝑚𝑒𝑎𝑛 − ( μ 1 − μ 2 ) √ ( 𝑠 1 2 𝑛 1 + 𝑠 2 2 𝑛 2 ) where s1 2 ,s2 2 is the sample variance of the sample 1 and sample 2, 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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