Question

1. A sample of 40 runners will be used to compare two new routines for stretching. The runners will be randomly assigned to one of the routines which they will follow for two weeks. Satisfaction with the routines will be measured using a questionnaire at the end of the two-week period. For the first routine, nine runners said that they were satisfied or very satisfied. For the second routine, six runners said that they were satisfied or very satisfied.

a) What is the test statistic?

b) What is the p-value?

Answer 1

To Test :-

H0 :- P1 = P2
H1 :- P1 ≠ P2

Part a)

p̂1 = 9 / 40 = 0.225
p̂2 = 6 / 40 = 0.15
Test Statistic :-
Z = ( p̂1 - p̂2 ) / √( p̂ * q̂ * (1/n1 + 1/n2) ))
p̂ is the pooled estimate of the proportion P
p̂ = ( x1 + x2) / ( n1 + n2)
p̂ = ( 9 + 6 ) / ( 40 + 40 )
p̂ = 0.1875
q̂ = 1 - p̂ = 0.8125
Z = ( 0.225 - 0.15) / √( 0.1875 * 0.8125 * (1/40 + 1/40) )
Z = 0.8593

Part b)

P value = 2 * P ( Z < 0.8593 ) = 0.3902 ( From Z table )