Question

A retail company has started a new advertising campaign in order to increase sales. In past, the mean spending in both the 18–35 and 35+ age groups was at most $70.00. a. Formulate a hypothesis test to determine if the mean spending has statistically increased to more than $70.00. b. After the new advertising campaign was launched, a marketing study found that the sample mean spending for 300 respondents in the 18–35 age group was $78.56, with a sample standard deviation of $59.90. Is there sufficient evidence to conclude that the advertising strategy significantly increased sales in this age group with significance level of 5%? c. For 700 respondents in the 35+ age group, the sample mean and sample standard deviation were $65.83 and $42.59, respectively. Is there sufficient evidence to conclude that the advertising strategy significantly increased sales in this age group with significance level of 5%?

Answer 1

a) Null and alternative hypothesis:

b)

Test statistic:

df = 300-1 = 299

p-value = T.DIST.RT(2.4752,299) =  0.0069

Conclusion:

As p-value = 0.0069 <0.05, we reject the null hypothesis.

There is sufficient evidence to conclude that the advertising strategy significantly increased sales in this age group with significance level of 5%.

c)

Test statistic:

df = 700-1 = 699

p-value = T.DIST.RT(-2.5905, 699) =  0.9951

Conclusion:

As p-value = 0.9951 > 0.05, we fail to reject the null hypothesis.

There is not sufficient evidence to conclude that the advertising strategy significantly increased sales in this age group with significance level of 5%.