A marketing firm wants to know if there is a difference in the best marketing strategy for new customers compared to returning customers. In order to determine the relationship between marketing strategy and customer type, the following information on number of sales generated is obtained for each group. Is there sufficient evidence at the 0.10.1 level of significance to conclude that an association exists between marketing strategy and customer type? Observed Sample of CustomersPaid searchSocial mediaWeb retargetingTotalNew customer

140

169

164

473

Returning customer

166

141

149

456

Total

306

310

313

929 Calculate the expected value for the number of sales generated by the social media strategy for new customers. Round your answer to six decimal places.

To calculate the expected value for the number of sales generated by the social media strategy for new customers, we need to apply the formula for the expected value in a contingency table:

\[
E = \frac{{\text{{Row total}} \times \text{{Column total}}}}{\text{{Overall total}}}
\]

Where:
- **Row total** is the total number of new customers.
- **Column total** is the total number of customers generated from social media.
- **Overall total** is the total number of customers.

### Step 1: Identify the necessary values
- **Row total (new customers)**: 473
- **Column total (social media)**: 310
- **Overall total**: 929

### Step 2: Calculate the expected value
Now, substitute the values into the formula:

\[
E = \frac{473 \times 310}{929}
\]

Let’s compute that.

The expected value for the number of sales generated by the social media strategy for new customers is approximately **157.836383**.

Would you like more details on this calculation or have any further questions?

Here are five related questions that can expand on this:
1. How do we interpret the expected value in a contingency table?
2. How can we perform a chi-square test to determine if there's an association between customer type and marketing strategy?
3. What is the formula for calculating the chi-square statistic?
4. How do we determine the degrees of freedom in a contingency table test?
5. What are the implications of a significant result in a chi-square test?

**Tip:** When analyzing contingency tables, always compare observed values with expected values to determine if there's a significant difference.

A marketing firm wants to know if there is a difference in the best marketing strategy for new customers compared to returning customers. In order to determine the relationship between marketing strategy and customer type, the following information on number of sales generated is obtained for each group. Is there sufficient evidence at the 0.10 level of significance to conclude that an association exists between marketing strategy and customer type? Observed Sample of Customers: Paid search (new customer: 140, returning customer: 166), Social media (new customer: 169, returning customer: 141), Web retargeting (new customer: 164, returning customer: 149). Total: New customer (473), Returning customer (456), Overall total (929). Calculate the expected value for the number of sales generated by the social media strategy for new customers. Round your answer to six decimal places.

This page demonstrates how to calculate the expected value of social media sales for new customers based on a contingency table. The problem involves marketing strategies and customer types, using the formula E = (Row total × Column total) / Overall total. Suitable for college-level statistics.

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