Question

The results of a mathematics placement exam at two different campuses of Mercy College follow:

Campus	Sample size	Mean	Population Std. Deviation
1	1,533	32	19
2	294	29	17

Is there a difference in the mean score of Campus 1 and Campus 2 of Mercy College? Given that the two population standard deviations are known, what is the p-value?

1.0129

0.0066

0.1129

1.0000

Answer 1

Solution:

Given that,

= 32

= 29

= 19

= 11

n₁ = 1533

n₂ = 294

This is a two tailed test

The null and alternative hypothesis is,

Ho: =

H_a :

The test statistic

z = ( - ) / ( / n₁) + ( / n₂ )

= ( 32 - 29 ) / ( 19²/1533) + ( 11² / 294)

= 2.718

p-value = 2*P(Z > z )

= 2*(1 - P(Z < z ))

= 2*( 1- P(Z < 2.718))

= 2*( 1 - 0.9967)

= 2* 0.0033

= 0.0066

The p-value is 0.0066