Yes, there is a significant decrease in the mean daily revenue after the price increase. The p-value is 9.0257e-06, which is less than 0.05.
To determine whether there has been a significant decrease in the mean daily revenue after the price increase, we can perform a two-sample t-test. Here's the hypothesis testing procedure:
1. Null Hypothesis (H₀): There is no difference in the mean daily revenue before and after the price increase. Symbolically, H₀: μ₁ - μ₂ = 0, where μ₁ is the mean daily revenue before the price increase and μ₂ is the mean daily revenue after the price increase.
2. Alternative Hypothesis (H₁): The mean daily revenue has decreased after the price increase. Symbolically, H₁: μ₁ - μ₂ > 0.
3. Significance Level (α): Let's assume α = 0.05.
4. Test Statistic: The t-test statistic is given by the formula:
t = (X₁ - X₂) / (s / √n)
where:
- X₁ is the mean daily revenue before the price increase ($75.00)
- X₂ is the mean daily revenue after the price increase ($70.00)
- s is the pooled standard deviation
- n is the total sample size (41 days)
5. P-value: The p-value is the probability of obtaining a test statistic as extreme or more extreme than the observed one, assuming the null hypothesis is true. A small p-value indicates that the observed difference is unlikely to have occurred by chance alone, providing evidence against the null hypothesis.
6. Decision: Compare the p-value to the significance level (α).
- If p-value ≤ α, reject the null hypothesis and conclude that there is a significant decrease in the mean daily revenue after the price increase.
- If p-value > α, fail to reject the null hypothesis and conclude that there is not enough evidence to support the claim that the mean daily revenue has decreased.
Calculating the test statistic and p-value using the given data:
t = (75.00 - 70.00) / (4.10 / √41) = 2.44
p-value ≈ 0.019
Since the p-value (0.019) is less than the significance level (0.05), we reject the null hypothesis and conclude that there is a significant decrease in the mean daily revenue after the price increase. This suggests that the price increase has negatively impacted the organization's revenue.