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a) Suppose that the heights of UW students are normally distributed with known population variance (o2 = 9). Based on 16 observations, the population mean is estimated to be 175 (i.e., / = 175) and the population variance is estimated to be 9 (i.e., 62 =9). Derive a 95% confidence interval for the population mean (M).
b) Suppose that the heights of UW students are normally distributed with unknown population variance. Based on 16 observations, the population mean is estimated to be 175 (i.e., / = 175) and the population variance is estimated to be 9 (i.e., 62 =9). Derive a 95% confidence interval for the population mean (M).
c) 95% confidence band from Question b) is wider than that from Question a). Provide an intuition about why this is the case.
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