# ch3-2 - Chapter 3 Review of Statistics(Part 2 Condence...

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Chapter 3 Review of Statistics (Part 2)

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Confidence Intervals for the Population Mean It is impossible to know the true population mean μ Y from random samples. However, it is possible to construct an interval that contains μ Y with a prespecified probability. I The prespecified probability is called the confidence level . I The interval is called the confidence interval . 95% confidence interval for μ Y is Y ° 1.96 SE ( Y ) ± μ Y ± Y + 1.96 SE ( Y ) or μ Y = ° Y ² 1.96 SE ( Y ) ± . The interval contains the true μ Y in 95% of all possible random samples.
Comparing Means from Different Populations: Hypothesis Tests Do recent male and female college graduates earn the same amount on average? I Let μ w be the mean hourly earning in the population of women recently graduated. I Let μ m be the population mean for recently graduated men. The null and the two-sided alternative hypothesis for our question are: H 0 : μ m ° μ w = 0 vs. H 1 : μ m ° μ w 6 = 0. Population means are unknown, we have to estimate them from samples.

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Comparing Means from Different Populations: Hypothesis Tests An estimator of μ m ° μ w is Y m ° Y w where Y m and Y w are the sample average for men and women. I To test the null hypothesis, we need to know the distribution of Y m ° Y w . Suppose we have samples of n m men and n w women. I Y m is approximately distributed N ( μ m , σ 2 m / n m ) , where σ 2 m is the population variance I Y w is approximately distributed N ( μ w , σ 2 w / n w ) ,where σ 2 w is the population variance.
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