Question

A retail company has started a new advertising campaign in order to increase sales. In the 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 400 respondents in the 18–35 age group was $73.65, with a sample standard deviation of $56.60. Is there sufficient evidence to conclude that the advertising strategy significantly increased sales in this age group with significance level of 5%?

c. For 600 respondents in the 35+ age group, the sample mean and sample standard deviation were $73.42 and $45.44, 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) Hypothesis: Vs  

b) Given : Sample size=n=400

Sample mean=

Sample standard deviation=s=56.60

Hypothesized value=

Significance level=

The test statsitic is ,

d.f.=degrees of freedom=n-1=400-1=399

The critical value is ,

; From Excel "=TINV(2*0.05,399)"

Decision : Here , the value of the test statistic does not lies in the rejection region.

Therefore , fail to reject the null hypothesis.

Conclusion : Hence , there is not sufficient evidence to conclude that the advertising strategy significantly increased sales in this age group.

c) Given : Sample size=n=600

Sample mean=

Sample standard deviation=s=45.44

Hypothesized value=

Significance level=

The test statsitic is ,

d.f.=degrees of freedom=n-1=600-1=599

The critical value is ,

; From Excel "=TINV(2*0.05,599)"

Decision : Here , the value of the test statistic lies in the rejection region.

Therefore , reject the null hypothesis.

Conclusion : Hence , there is sufficient evidence to conclude that the advertising strategy significantly increased sales in this age group.