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Solution 2

# Solution 2 - IE4230 Homework 2 1 The heights of 10 students...

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IE4230 Homework 2 27/01/2015

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1. The heights of 10 students are shown in Table 1. a) Calculate the sample average and sample variance. The formulas for sample mean and sample variance are: Student Height H i -Mean (H i -Mean) 2 1 169 -0.4 0.16 2 167 -2.4 5.76 3 165 -4.4 19.36 4 172 2.6 6.76 5 171 1.6 2.56 6 170 0.6 0.36 7 166 -3.4 11.56 8 174 4.6 21.16 9 171 1.6 2.56 10 169 -0.4 0.16 Sum 1694 70.4 Mean 169.4 Variance 7.8222 =average(…) =variance(…) 2 2 1 1 1 1 and 1 n n i i i i x x s x x n n
Sampling for normal If X n are independent and normally distributed 𝑁 𝜇, 𝜎 2 , 𝑋 and 𝑆 2 are the sample mean and sample variance respectively, then we have Z = 𝑋 −𝜇 𝜎/ 𝑛 ~𝑁 0,1 𝑛−1 𝜎 2 𝑆 2 ~𝜒 2 𝑛 − 1 T = 𝑋 −𝜇 𝑆/ 𝑛 ~𝑡(𝑛 − 1)

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b) Assume that the student heights are independently normal distributed. Construct 95% confidence intervals on the mean and variance. Since the true parameter values of the mean and variance are unknown, we have The 100(1- α )% two-sided confidence intervals can be constructed by
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