(Solution) - For a random sample of 20 data pairs the sample -(2025 Original AI-Free Solution)

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Academic Level: Undergrad. (yrs 3-4)

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For a random sample of 20 data pairs, the sample mean of the differences was 2. The sample standard deviation of the differences was 5. Assume that the distribution of the differences is mound-shaped and symmetrical. At the 1% level of significance, test the claim that the population mean of the differences is positive.
(a) Is it appropriate to use a Student?s t distribution for the sample test statistic? Explain. What degrees of freedom are used?
(b) State the hypotheses.
(c) Compute the sample test statistic.
(d) Estimate the P-value of the sample test statistic.
(e) Do we reject or fail to reject the null hypothesis? Explain.
(f) What do your results tell you?