HW4 SOLUTIONS Inference for Population Mean 1. List all the assumptions that need met in order for a t distribution based inference to be valid. Correct: data must be from a random sample from a large population observations within the sample must be independent n small - population distribution must be approximately normal n large - population distribution need not be approximately normal (CLT kicks in) 2. The blood pressure (average of systolic and diastolic measurements) of each of 38 randomly selected persons was measured. The average was 94.5 mm Hg and the standard deviation 8.0497 mm Hg. a. Construct a 95% confidence interval for the true mean blood pressure. Correct: TI-84 STAT->TESTS and T-interval->Enter->Stats->Enter->Scroll down to enter sample mean, sample sd, and sample size, C-Level: .95->highlight Calculate->Enter yields (91.854, 97.146) b. Interpret the interval you just computed in part (a). Correct: We are 95% confident that true mean blood pressure for people like the ones used in this study is at least 91.854 mm Hg and at most 97.146 mm Hg. c. Use the QQplot to comment on whether it appears the assumption of normality has been violated. Correct: Goal: We need to check the assumption that ݔ̅has a normal distribution. We get that one of two ways: 1)Either the data that created ݔ̅is from a normal distribution 2)Or the sample size is large enough for the CLT to “kick in” Step 1 – Check the QQ plotI see no systematic departure from the line, except for that little blip in the upper end of the distribution. Step 2 – Can we call the CLT? Mainly, the points form a linear pattern and our sample size is 38, so the CLT should kick in anyway. Conclusion: I do not see evidence against normality of ݔ̅- it should be just fine to proceed with this t distribution based procedure.
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