Question

SAT test scores are reported to follow a normal distribution with variance 125. A re- searcher questions if the assumed variance ought to be lower, and randomly samples 20 test scores. The sample variance of the 20 scores is 104. = 0.95a = 0.05 = 0.025 a0.975 30.144 v19 8.907 10.117 32.852 V = 20 9.591 10.851 31.410 34.170 Test whether the researcher is justified at the 5% significance level

Answer 1

null hypothesis:     Ho:				σ2 =	125
Alternate hypothesis: Ha:				σ2 <	125

at 0.05 level and (n-1=19) df crtiical value=					10.1170
Decision rule:reject Ho if test statistic X2 in critical region:				X2	<	10.117

test stat :

=χ2=(n-1)s2/σ2=9*104/125 =

15.808

as test statistic is not in critical region, we can not reject null hypotheiss.

we do not have evidence to conclude that researcher is justified that variance is less than 125