A small business tracks how advertising spending relates to weekly sales.
$\left(D\right)$ Are the actual sales numbers for weeks with \$400 ad-spending within the interval?

• A. Yes
• B. No
• C. More info is required

Answer: (A)

Verified step by step guidance

1. Step 1: Understand the problem context. We have data on weekly advertising spending and corresponding sales. The question asks if the actual sales for weeks with \$400 advertising spending fall within a certain prediction interval.
2. Step 2: Identify the weeks with \$400 advertising spending from the table. From the data, week 13 has advertising spending of \$400 with sales of 10200.
3. Step 3: To determine if the actual sales fall within the interval, we need to calculate the prediction interval for sales when advertising spending is \$400. This involves fitting a linear regression model with advertising as the independent variable and sales as the dependent variable.
4. Step 4: Using the regression model, calculate the predicted sales for \$400 advertising spending. Then, compute the prediction interval around this predicted value, which accounts for both the uncertainty in the regression estimate and the variability of individual sales values.
5. Step 5: Compare the actual sales value (10200) for week 13 to the calculated prediction interval. If 10200 lies within the interval, the answer is 'Yes'; otherwise, 'No'.