Question

14. For a class of 36 students, the standard deviation score of exam 2 is 15.

a) Find the critical values χ²_L and χ²_R for the 98% confidence level.

b) Create the 98% confidence interval for the population standard deviation of exam scores. Is it possible for the class to have a standard deviation of exam scores 18 by the end of the semester?

Answer 1

#Solution:

chi sq L=1-alpha/2,n-1

chi sqR=alpha/2,n-1

alpha=0.02

alpha/2=0.02/2=0.01

1-0.01=0.99,35 df

so ==CHISQ.INV.RT(0.99,35)=18.50892623

0.01,35 df

so ==CHISQ.INV.RT(0.01,35)=57.34207343

SOlution-b:

98% confidence interval for sigma is

sqrt(n-1)*s^2/<sigma<sqrt((n-1)*s^2/

=sqrt(36-1)*15^2/57.34207343)<sigma<sqrt((36-1)*15^2/18.50892623)

11.7189<sigma<20.6269

98% lower limit for sigma=11.7189

98% upper limit for sigma=20.6269

Given sd=18 is in the 98% confidence interval range

11.7189<18<20.6269

So it is possible for the class to have a standard deviation of exam scores 18 by the end of the semest