College students' annual earnings: 98% confidence; n = 9, x = $3361, s = $865 a) $546 < σ < $1907 b) $526 < σ < $1693 c) $681 < σ < $1128 d) $584 < σ < $1657

Question

I need to find X2l and X2R for this Question!

Answer 1

The right chi-squared critical value for alpha/2=0.01 is 1.647 (98% confidence level) with n-1=8 degrees of freedom left chi-squared value is 20.09 for 1-alpha/2=0.99. Using the formula, (a) is the correct answer:

√((n-1)s²/χ²L)<σ<√((n-1)s²/χ²R, √(8×865²/20.09)<σ<√(8×865²/1.647), $546<σ<$1907.

The confidence level is the interval between the left and right chi-squared values, hence the reason for halving alpha.