Question

The aim is to measure if an advertising campaign changes the preferences of consumers
of a product. A random sample is selected before the advertising campaign and
they measure preferences. The advertising campaign is carried out and then the preferences are measured
again from the consumers. The results are shown in the next table.
before the campaign After the campaign
Sample size 300 450
People who bought the product 100 200
a) Use the hypothesis testing procedure to determine if the advertising campaign
improves consumer preferences for the product in question. Use a level of
5% significance.
Establish the hypothesis:

Test the hypothesis:
Decision:

Conclusion:

Answer 1

a)

Establish the hypothesis:

Let P_B and P_A be the proportion of people who bought the product before and after the campaign respectively.

Null hypothesis H0:  P_A = P_B

Alternative hypothesis H0:  P_A > P_B

Test the hypothesis:

Let nA and nB be the sample sizes  before and after the campaign respectively.

Sample proportions,

P_A ​​​​​​​ = 200 / 450 = 0.4444444

P_B = 100 / 300 = 0.3333333

Pooled proportion, p = (nA P_A ​​​​​​​+ nB P_B​​​​​​​) / (nA + nB)

= (450 * 0.4444444 + 300 * 0.3333333) / (450 + 300)

= 0.4

Standard error of differences in proportion, p =

УР(1 _ p) * ((1/n..) + (1/nB)) = V 0.4(1-0.4) ,* ( (1 /450) + (1/300) )

= 0.0365

Test statistic, z = (P_A ​​​​​​​ - P_B) / SE

= (0.4444444 - 0.3333333) / 0.0365

= 3.04

P-value = P(z > 3.04) = 0.0012

Decision:

Since p-value is less than 0.05 significance level, we reject null hypothesis H0

Conclusion:

We conclude that there is significant evidence that proportion of people who bought the product after the campaign is greater than that before the campaign.