Question

13. Based on a random sample of size 20 from a normal distribution with variance o?, the width of the 95% confidence interval for ois 150. Let xã, be the the critical value of a chi-squared random variable with v degrees of free- dom. The following table lists values of x. for specific combinations of a and v: v = 19 v = 20 a = 0.975 8,907 9.591 a = 0.95 10.117 10.851 a = 0.05 30.144 3 1.410 a = 0.025 32.852 34.170 Det er mine the unbiased sample variance calculated from the sample,

Answer 1

solution: Given that Sample size ne 90 confidence interval 95% for ou is 150 x=0.975 x=0.952=0.05&=0.025 10.117 30.144 32-852 v=19 34.170 8.907 9.591 10.851 31.4107 V=20 confidence Interval for a population Variance. (n-1) § or (n-1) 5' Xala x,- 2/2 where Š is the unbiased variance width of the confidence interval. (0-13 (n-1)3 = 150 2 0/2 X 212 {0198" ( termine tavs] - 150 Lxxl : n=90 x= = 1-0.95 0.05

= 0.025 = 1-0.025 India = 0.975 d = degree of freedom n-1 20-1 21-012=X0.975 = 8.907 (from above table.). xdlr X0.025 = 32.852 (from above tables 150 še (201) Citron shoes 150 C92852 -8.9077 292.612764 150 19 (23.9457 1292-6127641

150 19 (0.0818317) 150 1.554802305206344 96-47528788 ~ 196.475 The untirised sample variance is 196.4751