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# Test of hypothesis, Confidence interval

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The data in the table below (you may assume these to be normally distributed) give the iron intakes, in milligrams, in a 24 hour period for 45 randomly selected adult females under the age of 51.

15.0 18.1 14.4 14.6 10.9 18.1 18.2 18.3 15.0
16.0 12.6 16.6 20.7 19.8 11.6 12.8 15.6 11.0
15.3 9.4 19.5 18.3 14.5 16.6 11.5 16.4 12.5
14.6 11.0 12.5 18.6 13.1 12.1 10.7 17.3 12.4
17.0 6.3 16.8 12.5 16.3 14.7 12.7 16.3 11.5

Obtain the sample mean and variance for this data, and test the hypothesis that the corresponding population mean is 18. Perform your test by:

a) assuming that the computed sample variance is the known population variance;
b) without assuming the variance is known, i.e., employing a t-test. Find also two 99% confidence intervals for the population mean; the first (as in question a)) assuming that the variance is known; the second without assuming known variance.