A market research firm wants to find out if men and women fe

A market research firm wants to find out if men and women feel differently about SilkyTouch facial tissues. In a survey of 100 men, 75% said they had a favorable impression of SilkyTouch. Out of 150 surveyed women, 65% said they had a favorable impression of SilkyTouch. At a 95% confidence level, which conclusion should the research firm draw?

Answer: Do not reject the null of no difference between males and females.

Solution

Let p1 be the proportion for men

Let p2 be the proportion for women

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)

=(0.75-0.65)/sqrt(0.75*0.25/100+0.65*(1-0.65)/150)

=1.72

It is a two-tailed test.

Given a=1-0.95=0.05, 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 the null hypothesis.

Since Z=1.72 is between -1.96 and 1.96, we do not reject the null hypothesis.

So we can conclude that there is no difference between males and females