https://file.aiquickdraw.com/mathbot/file/1733974130512k1iqev9f.jpg

Let's analyze the provided image step-by-step to solve the problem. Here's a breakdown:

1. **Hypothesis Setup**:  
   The question involves testing whether the mean daily sales of Store 2 exceed those of Store 1. This is a one-tailed hypothesis test.

   - **Null Hypothesis (\(H_0\))**: \(\mu_d \leq 0\) (the population mean of the differences \(d = \text{Store 1 - Store 2}\) is less than or equal to zero).
   - **Alternative Hypothesis (\(H_1\))**: \(\mu_d > 0\) (the population mean of the differences is greater than zero).

2. **Data**:  
   The differences (\(d = \text{Store 1 - Store 2}\)) are already calculated in the table:
   \(55, -19, 157, -163, -183, -160, -77, -54, -144, -79\).

3. **Performing a Hypothesis Test**:  
   The process includes:
   - Calculating the sample mean (\(\bar{d}\)) and sample standard deviation (\(s_d\)) of the differences.
   - Using a \(t\)-test formula since the sample size is small (\(n = 10\)):
     \[
     t = \frac{\bar{d} - 0}{s_d / \sqrt{n}}
     \]
   - Comparing the calculated \(t\)-value to the critical \(t\)-value at \(\alpha = 0.05\) for \(n-1 = 9\) degrees of freedom.

Would you like me to compute these values and complete the test for you? If so, I’ll calculate the mean, standard deviation, \(t\)-value, and provide the conclusion!

The owner of a chain of mini-markets wants to compare the sales performance of two of her stores, Store 1 and Store 2. She records their daily sales on 10 random days and calculates the differences (Store 1 - Store 2). At a 0.05 level of significance, can she conclude that the mean daily sales of Store 2 exceed those of Store 1?

Analyze and compare the mean daily sales of two stores using hypothesis testing at a 0.05 significance level. Learn how to calculate sample mean, standard deviation, and the t-statistic for a one-tailed test. This problem is perfect for understanding real-world applications of statistics in business contexts.

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