Question

A statistics teacher believes that students in an evening statistics class score higher than the students in a day class. The results of a special exam are shown below. Test the teachers claim using a level of confidence of 0.05.  

Day Students                   EveningStudents

     n1 = 36                           n2 = 41                                           

      x1 = 96                         x2 = 99

s1 = 5.8                         s2 = 6.3

a) Give the Ho and Ha and label which is the claim

b) give the pvalue

c) give the final decision about the claim.

Answer 1

a)

H0 : mu1 =mu2
Ha: mu1 < mu2

b)

test statistics:

t = (x1 -x2)/sqrt(s1^2/n1+s2^2/n2)
= (96 - 99)/sqrt(5.8^2/36 + 6.3^2/41)
= -2.175

SE = sqrt[ (s12/n1) + (s22/n2) ]
(s12/n1)	1.2938
(s22/n2)	0.9680
SE	1.5040
DF = (s12/n1 + s22/n2)2 / { [ (s12 / n1)2 / (n1 - 1) ] + [ (s22 / n2)2 / (n2 - 1) ] }
[ (s12 / n1)2 / (n1 - 1) ]			0.067
[ (s22 / n2)2 / (n2 - 1) ]			0.02
(s12/n1 + s22/n2)2			5.12
DF =	57

p value = 0.0169

c)

Reject H0 as p value < 0.05