8.1.3 Practical Example

Let us explore the application of a one-sample t-test in a practical business scenario. Consider our previous digital marketing example, where a company’s marketing team has implemented an advertising campaign aimed at increasing customer purchases beyond 50 purchases per customer. To assess the campaign’s effectiveness, they have collected data from a sample of 80 customers. Download the Excel file to review the data. Excel file: Digital marketing  (You may have already downloaded this file when working through Section 5.3.)

The marketing executive believes the campaign has been successful, hypothesising that the average number of purchases per day has increased compared to the pre-campaign average. They want to test this claim rigorously, using a 95% confidence level.

This scenario presents an ideal opportunity to apply the one-sample t-test, a statistical tool that allows us to determine whether a sample mean significantly differs from a known or hypothesised population mean.

Step 1: Formulate the Hypotheses

• H₀: μ ≤ 50
• H₁: μ > 50

This formulation represents a one-tailed test, as we are specifically testing for an increase in purchases. The value 50 serves as our benchmark, possibly representing the pre-campaign average or a target set by the marketing team.

Step 2: Collect and Analyse Sample Data

In our digital marketing campaign example, we have gathered the following data:

n = 80

x̄ = 53.02

s = 10.22 (we are dealing with sample now, so you should use STDEV.S() function for finding standard deviation)

Step 3: Calculate the T-Statistic

To quantify the difference between our sample mean and the hypothesised population mean, we calculate the t-statistic using the formula:

Step 4: Determine t critical value:

For an upper tailed test with α = 0.05 and 79 degrees of freedom (n - 1), we input:

• =T.INV(0.95,79)

The formula will return the t critical value, which in this case would be approximately 1.664.

Step 5: Compare the T-Statistic to T Critical Value

We now compare our calculated t-statistic to the critical value:

• Calculated t-statistic: 2.647

• T Critical value: 1.646

Since our calculated t-statistic (2.647) is greater than the critical t-value (1.646), we reject the null hypothesis.

Step 6: Draw Conclusions and Interpret Results

Based on our analysis, we have strong statistical evidence to conclude that the true average number of customer purchases after the marketing campaign is significantly higher than 50.