Question

How can I determine if there is a significant difference with the following information using a two-tailed test and with alpha =.05

u=14

n=64

x bar=12.5

E = 4.8

Answer 1

We have to test

Ho :   = 14 Vs H1 : 14

Level of significance a = 0.05

Test statistic t

t = ( xbar - )/(s/√n)

t = ( 12.5-14)/(4.8/√64)

t test statistic = -2.5

tCritical for a = 0.05 and d.f = n -1 = 63

tCritical = t​​​​​​a/2, n -1 = t​​​​​​0.025, 63 = -2.00

Decision rule : we reject the null hypothesis Ho if t < -2.00 otherwise we fail to reject Ho

Our t = -2.5 < -2.00

Conclusion : Reject the null hypothesis Ho , there is significant difference