1.43 Parameters and statistics: Identify which value represents the sample mean and which value represents the claimed population mean. a) American households spent an average of about \$52 in 2007 on Halloween merchandise such as costumes, decorations and candy. To see if this number had changed, researchers conducted a new survey in 2008 before industry numbers were reported. The survey included 1,500 households and found that average Halloween spending was \( \$ 58 \) per household. The sample mean is 52 dollars, while the claimed population mean is \[ 203 \] dollars. b) The average GPA of students in 2001 at a private university was 3.37 . A survey on a sample of 203 students from this university yielded an average GPA of 3.59 in Spring semester of 2012. The sample mean is 3.56 and the claimed population mean is \[ 3.37 \] 3.37

Let's analyze each scenario to correctly identify the **sample mean** and the **claimed population mean**. --- ### **a) Halloween Merchandise Spending** **Scenario:** - **Claimed Population Mean (2007):** American households spent an average of **\$52** on Halloween merchandise. - **Survey (2008):** A new survey of **1,500 households** found an average spending of **\$58** per household. **Identification:** - **Claimed Population Mean:** This is the average spending reported for the entire population (all American households) in 2007, which is **\$52**. - **Sample Mean:** This is the average spending observed in the sample surveyed in 2008, which is **\$58**. **Summary:** - **Sample Mean:** \$58 - **Claimed Population Mean:** \$52 --- ### **b) Student GPA** **Scenario:** - **Claimed Population Mean (2001):** The average GPA of students at a private university was **3.37**. - **Survey (2012):** A survey of **203 students** yielded an average GPA of **3.59** in the Spring semester. **Identification:** - **Claimed Population Mean:** This is the average GPA reported for the entire population of students in 2001, which is **3.37**. - **Sample Mean:** This is the average GPA observed in the sample surveyed in 2012, which is **3.59**. **Summary:** - **Sample Mean:** 3.59 - **Claimed Population Mean:** 3.37 --- **Note:** It's essential to distinguish between the population mean (a value representing the entire group) and the sample mean (a value representing a subset of the group). In both scenarios, the sample mean is derived from the survey conducted later, while the population mean is the established average from an earlier time.