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[ (s_{1}^{2}/n_{1}) +
(s_{2}^{2}/n_{2}) ] |
||||

(s_{1}^{2}/n_{1}) |
1.2938 | |||

(s_{2}^{2}/n_{2}) |
0.9680 | |||

SE | 1.5040 | |||

DF =
(s_{1}^{2}/n_{1} +
s_{2}^{2}/n_{2})^{2} / { [
(s_{1}^{2} / n_{1})^{2} /
(n_{1} - 1) ] + [ (s_{2}^{2} /
n_{2})^{2} / (n_{2} - 1) ] } |
||||

[
(s_{1}^{2} / n_{1})^{2} /
(n_{1} - 1) ] |
0.067 | |||

[
(s_{2}^{2} / n_{2})^{2} /
(n_{2} - 1) ] |
0.02 | |||

(s_{1}^{2}/n_{1} +
s_{2}^{2}/n_{2})^{2} |
5.12 | |||

DF = |
57 |

p value = 0.0169

c)

Reject H0 as p value < 0.05

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