Business Context
RetailCo, a company selling home goods, is analyzing its monthly sales data to identify seasonal trends. The management suspects that sales may increase during the holiday season and wants to quantify this effect.
Given Data
| Month | Sales (in $) |
|---|
| Jan | 20000 |
| Feb | 21000 |
| Mar | 25000 |
| Apr | 23000 |
| May | 24000 |
| Jun | 30000 |
| Jul | 35000 |
| Aug | 32000 |
| Sep | 28000 |
| Oct | 40000 |
| Nov | 45000 |
| Dec | 60000 |
The company wants to determine if the increase in sales during the last quarter is statistically significant compared to the first quarter.
Requirements
- State the null and alternative hypotheses regarding the seasonal effect on sales.
- Calculate the average sales for Q1 (January - March) and Q4 (October - December).
- Perform a t-test to compare the means of sales between Q1 and Q4.
- Determine the p-value and make a decision regarding the null hypothesis at α = 0.05.
- Interpret the results in the context of RetailCo's business strategy.
Assumptions
- Sales data are normally distributed within each quarter.
- The sales observations are independent of each other.
