Question

The average height of students in a batch is 100 cm and the standard deviation is 15. However, Tedd believes that this has changed, so he decides to test the height of 75 random students in the batch. The average height of the sample comes out to be 105. Is there enough evidence to suggest that the average height has changed?

Answer 1

Null and alternative hypotheses

Ho : = 100

H1 : 100

Level of significance a = 0.05

Test statistic Z

Z = ( xbar - )/(/√n)

Z = ( 105 -100)/(15/√75)

Z = 2.89

Z critical value for a = 0.05 and two tailed test

Zcritical = Z​​​​​​a/2 = Z​​​​​​0.025

Zcritical = 1.96

Decision rule : Reject Ho if Z > 1.96 , otherwise we fail to reject Ho

Our Z = 2.89 > 1.96

Conclusion : Reject null hypothesis Ho , there is sufficient evidence to support the claim that the average height has changed