17 of 30 participants yawned when confronted with a picture

17 of 30 participants yawned when confronted with a picture of a yawning man, while 11 of 30 independent participants yawned when shown a picture of a yawning man with his eyes covered. is there evidence in these data that covering the yawning man\'s eyes in an image changes the occurrence of contagious yawns

Solution

p1=17/30=0.5666667

p2=11/30 =0.3666667

The test hypothesis:

Ho: p1=p2 (i.e. null hypothesis)

Ha: p1 not equal to p2 (i.e. alternative hypothesis)

The test statistic is

Z=(p1-p2)/sqrt(p1*(1-p1)/n1+p2*(1-p2)/n2)

=(0.5666667-0.3666667)/sqrt(0.5666667*(1-0.5666667)/30+0.3666667*(1-0.3666667)/30)

=1.58

Assume that the signifcant level a=0.05

It is a two-tailed test.

The critical values are Z(0.025) = -1.96 or 1.96 (from standard normal table)

The rejection regions are if Z<-1.96 or Z>1.96, we reject Ho.

Since Z=1.58 is between -1.96 and 1.96, we do not reject Ho.

So we can not conclude that there is evidence in these data that covering the yawning man\'s eyes in an image changes the occurrence of contagious yawns