Do shoppers at the mall spend the same amount of money on average the day after Thanksgiving compared to the day after Christmas? The 48 randomly surveyed shoppers on the day after Thanksgiving spent an average of $136. Their standard deviation was $37. The 41 randomly surveyed shoppers on the day after Christmas spent an average of $144. Their standard deviation was $45. What can be concluded at the a 0.01 level of significance? %3D For this study, we should use (Select an answer a. The null and alternative hypotheses would be: Ho: Select an answer Select an answer Select an answer | (please enter a decimal) H: (Select an answer | (Please enter a decimal) Select an answer Select an answer b. The test statistic ? (please show your answer to 3 decimal places.) C. The p-value = |(Please show your answer to 4 decimal places.) %3D d. The p-value is (? a e. Based on this, we should (Select an answer f. Thus, the final conclusion is that .. v the null hypothesis. The results are statistically significant at a = 0.01, so there is sufficient evidence to conclude that the mean expenditure for the 48 day after Thanksgiving shoppers that were observed is a different amount of money compared to the mean expenditure for the 41 day after Christmas shoppers that were observed. O The results are statistically insignificant at a = 0.01, so there is insufficient evidence to conclude that the population mean amount of money that day after Thanksgiving shoppers spend is a different amount of money compared to the population mean amount of money that day after Christmas shoppers spend. The results are statistically insignificant at a = 0.01, so there is statistically significant evidence to conclude that the population mean amqunt of money that day after Thanksgiving shoppers spend is equal to the population mean amount of money that day after Christmas shoppers spend.
Do shoppers at the mall spend the same amount of money on average the day after Thanksgiving compared to the day after Christmas? The 48 randomly surveyed shoppers on the day after Thanksgiving spent an average of $136. Their standard deviation was $37. The 41 randomly surveyed shoppers on the day after Christmas spent an average of $144. Their standard deviation was $45. What can be concluded at the a 0.01 level of significance? %3D For this study, we should use (Select an answer a. The null and alternative hypotheses would be: Ho: Select an answer Select an answer Select an answer | (please enter a decimal) H: (Select an answer | (Please enter a decimal) Select an answer Select an answer b. The test statistic ? (please show your answer to 3 decimal places.) C. The p-value = |(Please show your answer to 4 decimal places.) %3D d. The p-value is (? a e. Based on this, we should (Select an answer f. Thus, the final conclusion is that .. v the null hypothesis. The results are statistically significant at a = 0.01, so there is sufficient evidence to conclude that the mean expenditure for the 48 day after Thanksgiving shoppers that were observed is a different amount of money compared to the mean expenditure for the 41 day after Christmas shoppers that were observed. O The results are statistically insignificant at a = 0.01, so there is insufficient evidence to conclude that the population mean amount of money that day after Thanksgiving shoppers spend is a different amount of money compared to the population mean amount of money that day after Christmas shoppers spend. The results are statistically insignificant at a = 0.01, so there is statistically significant evidence to conclude that the population mean amqunt of money that day after Thanksgiving shoppers spend is equal to the population mean amount of money that day after Christmas shoppers spend.
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The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.
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![### Analyzing Consumer Spending: Thanksgiving vs. Christmas Shopping Habits
Below is a study examining whether there is a difference in spending habits between shoppers on the day after Thanksgiving compared to the day after Christmas.
**Research Question:**
Do shoppers at the mall spend the same amount of money on average the day after Thanksgiving compared to the day after Christmas?
#### Data:
- **Sample 1 (Day after Thanksgiving)**:
- Number of shoppers surveyed: 48
- Average spending: $136
- Standard deviation: $37
- **Sample 2 (Day after Christmas)**:
- Number of shoppers surveyed: 41
- Average spending: $144
- Standard deviation: $45
#### Hypothesis Test:
We will conduct a hypothesis test at the α = 0.01 significance level.
1. **Selection of Test:**
- For this study, we should use a **two-sample t-test**.
2. **Formulation of Hypotheses:**
- **Null Hypothesis (H₀):** \( \mu_1 = \mu_2 \)
- The mean amount of money spent by shoppers on the day after Thanksgiving is equal to the mean amount of money spent by shoppers on the day after Christmas.
- **Alternative Hypothesis (H₁):** \( \mu_1 \neq \mu_2 \)
- The mean amount of money spent by shoppers on the day after Thanksgiving is not equal to the mean amount of money spent by shoppers on the day after Christmas.
3. **Test Statistic:**
- The test statistic (t) is calculated as follows:
\[
t = \frac{(\bar{X}_1 - \bar{X}_2)}{\sqrt{(\frac{S_1^2}{n_1} + \frac{S_2^2}{n_2})}}
\]
- With \(\bar{X}_1 = 136\), \(\bar{X}_2 = 144\), \(S_1 = 37\), \(S_2 = 45\), \( n_1 = 48\), \( n_2 = 41 \), the t-statistic needs to be calculated.
4. **P-value:**
- Once the t-statistic is calculated, the p-value corresponding to this test statistic can be obtained.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffd16ddfa-c201-4e3f-90ee-e0e9ce8bf5de%2F862a1a17-cb34-4261-8469-dcf707a11192%2Fiz408jl_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Analyzing Consumer Spending: Thanksgiving vs. Christmas Shopping Habits
Below is a study examining whether there is a difference in spending habits between shoppers on the day after Thanksgiving compared to the day after Christmas.
**Research Question:**
Do shoppers at the mall spend the same amount of money on average the day after Thanksgiving compared to the day after Christmas?
#### Data:
- **Sample 1 (Day after Thanksgiving)**:
- Number of shoppers surveyed: 48
- Average spending: $136
- Standard deviation: $37
- **Sample 2 (Day after Christmas)**:
- Number of shoppers surveyed: 41
- Average spending: $144
- Standard deviation: $45
#### Hypothesis Test:
We will conduct a hypothesis test at the α = 0.01 significance level.
1. **Selection of Test:**
- For this study, we should use a **two-sample t-test**.
2. **Formulation of Hypotheses:**
- **Null Hypothesis (H₀):** \( \mu_1 = \mu_2 \)
- The mean amount of money spent by shoppers on the day after Thanksgiving is equal to the mean amount of money spent by shoppers on the day after Christmas.
- **Alternative Hypothesis (H₁):** \( \mu_1 \neq \mu_2 \)
- The mean amount of money spent by shoppers on the day after Thanksgiving is not equal to the mean amount of money spent by shoppers on the day after Christmas.
3. **Test Statistic:**
- The test statistic (t) is calculated as follows:
\[
t = \frac{(\bar{X}_1 - \bar{X}_2)}{\sqrt{(\frac{S_1^2}{n_1} + \frac{S_2^2}{n_2})}}
\]
- With \(\bar{X}_1 = 136\), \(\bar{X}_2 = 144\), \(S_1 = 37\), \(S_2 = 45\), \( n_1 = 48\), \( n_2 = 41 \), the t-statistic needs to be calculated.
4. **P-value:**
- Once the t-statistic is calculated, the p-value corresponding to this test statistic can be obtained.
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