Question

The following values are drawn from a normal population. (You may find it useful to reference the appropriate table: chi-square table or table) 35 22 22 30 1930 1919 Click here for the Excel Data File a. Calculate the point estimates for the population variance and the population standard deviation (Round your answers to 4 decimal places.) Point Estimates Population variance Population standard deviation b. Construct the 95% confidence interval for the population variance and the population standard deviation (Round intermediate calculations to at least 4 decimal places and final answer to 2 decimal places.) Confidence interval Population variance Population standard deviation

Answer 1

S.NO CUAWN- oo88NNXX (X-X) 10.500 -2.500 -2.500 5.500 -5.500 5.500 -5.500 -5.500 z(X-) = s=2(x-x)*(n-1)= s=\s2 = (X-R) 110.25000 6.25000 6.25000 30.25000 30.25000 30.25000 30.25000 30.25000 274.0000 39. 14286 6.2564 196 24.5000 Xezx/n

a) popuilation variance =39.1429

standard deviation =6.2564

b)

Critical value of chi square distribution for n-1=7 df and 95 % CI
Lower critical value χ2L=		1.690
Upper critical valueχ2U=		16.013

from above 95% confidence interval for population variance =(17.11<σ2<162.14)

95% confidence interval for population standard deviation =(4.14<σ<12.73)