Question

The mean weekly sales of a 4-wheeler was 50 units per agency in 20 agencies. After an advertising campaign, the mean weekly sales increased to 55 units per agency with a standard deviation of 10 units. Test whether the advertising campaign was successful.
[Given \( \sqrt{5} = 2.24 \), \( t_{19}(0.05) = 1.729 \)]

Hint:

For hypothesis testing, compare the calculated \( t \)-value with the critical \( t \)-value from the table. Reject \( H_0 \) if \( t \)-statistic exceeds the critical value.

Answer 1

Step 1: Null hypothesis \( H_0 \): The advertising campaign was not successful, represented by \( \mu = 50 \).
Step 2: Alternative hypothesis \( H_1 \): The advertising campaign was successful, represented by \( \mu>50 \).
Step 3: Calculate the \( t \)-statistic: \[ t = \frac{\bar{x} - \mu}{s / \sqrt{n}} = \frac{55 - 50}{10 / \sqrt{20}} = \frac{5}{10 / 4.47} = \frac{5 \cdot 4.47}{10} = 2.235. \]
Step 4: Compare the calculated \( t \)-statistic with the critical value \( t_{19}(0.05) \): As \( t = 2.235 \) is greater than \( t_{19}(0.05) = 1.729 \), we reject \( H_0 \).
Step 5: Conclusion: The advertising campaign was successful.