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For a random sample of 36 data pairs, the sample mean of the differences was 0.71. The sample standard deviation of the differences was 2. At the 5% level of significance, test the claim that the population mean of the differences is different from 0. In USE SALT (a) Is it appropriate to use a Student's t distribution for the sample test statistic? Explain. O No, the sample size is not larger than 30. O Yes, the sample size is larger than 30. O Yes, the standard deviation is larger than the sample mean. O No, the standard deviation is not smaller than the sample mean. What degrees of freedom are used? (b) State the hypotheses. OH: H = 0 ; H 1 : H d > 0 OH : Hd = 0 ; H ,: H 0.500