Question

Consider a study on the impact of using celebrities in television advertisements. A researcher investigated the relationship between gender of a viewer and the viewer’s brand awareness. Three hundred TV viewers were asked to identify product advertised by male celebrities. The data were summarized in the following table. Gender Male Female Totals Brand Awareness Could Identify Product 95 41 136 Could Not Identify Product 55 109 164 Totals 150 150 300

a. Is there evidence of a difference between males and females in the proportion who could identify product advertised by male celebrities? Set up the null and alternative hypotheses to gain insights into the impact of using celebrities in television advertisements.

b. Conduct the hypothesis test defined in (a), using the 0.05 level of significance.

c. Conduct the hypothesis test defined in (a), using the 0.01 level of significance.

d. Are the results of the hypothesis tests different for (b) and (c)?

Answer 1

Ans:

Gender	male	female	Totals
indentify	95	41	136
not identify	55	109	164
Total	150	150	300

a)

sample proportion for males who identify=95/150=0.6333

sample proportion for males who identify=41/150=0.2733

pooled proportion=136/300=0.4533

Test statistic:

z=(0.6333-0.2733)/sqrt((0.4533*(1-0.4533)*((1/150)+(1/150))

z=6.26

p-value(2 tailed)=2*P(z>6.26)=0.0000

b)

As,p-value<0.05,we reject the null hypothesis.

There is sufficient evidence to conclude that there is difference between males and females in the proportion who could identify product advertised by male celebrities.

c)

As,p-value<0.01,we reject the null hypothesis.

There is sufficient evidence to conclude that there is difference between males and females in the proportion who could identify product advertised by male celebrities.

c)No,result is same.