Question

Approximately 1 in 10 consumers favor cola brand A. After a promotional campaign in a sales region, 200 cola drinkers were randomly selected from consumers in the market area and were interviewed to determine the effectiveness of the campaign. The result of the survey showed that a total of 26 people expressed a preference for cola brand A. Do these data present sufficient evidence to indicate an increase in the acceptance of brand A in the region? Use α=0.05.

Answer 1

As we are testing here whether there is an increase in preference for cola brand A, therefore the null and the alternative hypothesis here are given as:

The sample proportion here is computed as:
p = x/n = 26/200 = 0.13

The test statistic here is computed as:

As this is a one tailed test, the p-value here is obtaiend from the standard normal tables as:
p = P(Z > 1.4142) = 0.0786

As the p-value here is 0.0786 > 0.05 which is the level of significance, therefore the test is not significant here and we cannot reject the null hypothesis here. Therefore we have insufficient evidence here that there is an increase in the acceptance of brand A in the region