Does the average Presbyterian donate more than the average Catholic in church on Sundays? The 56 randomly observed members of the Presbyterian church donated an average of $21 with a standard deviation of $5. The 46 randomly observed members of the Catholic church donated an average of $16 with a standard deviation of $15. What can be concluded at the a = 0.01 level of %3D significance? a. For this study, we should use ( Select an answer b. The null and alternative hypotheses would be:
Does the average Presbyterian donate more than the average Catholic in church on Sundays? The 56 randomly observed members of the Presbyterian church donated an average of $21 with a standard deviation of $5. The 46 randomly observed members of the Catholic church donated an average of $16 with a standard deviation of $15. What can be concluded at the a = 0.01 level of %3D significance? a. For this study, we should use ( Select an answer b. The null and alternative hypotheses would be:
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I need help with this question for parts b-d
Transcribed Image Text:**Comparison of Average Sunday Church Donations: Presbyterians vs. Catholics**
*Research Question:*
Does the average Presbyterian donate more than the average Catholic in church on Sundays?
*Study Details:*
- **Presbyterian Donations:**
- Sample Size: 56 members
- Average Donation: $21
- Standard Deviation: $5
- **Catholic Donations:**
- Sample Size: 46 members
- Average Donation: $16
- Standard Deviation: $15
*Analysis at α = 0.01 Level of Significance:*
1. **Statistical Test Selection:**
- For this study, we need to use a **two-sample t-test**.
2. **Hypotheses:**
- **Null Hypothesis (H₀):**
- μ₁ ≤ μ₂ (The mean donation by Presbyterians is less than or equal to the mean donation by Catholics)
- **Alternative Hypothesis (H₁):**
- μ₁ > μ₂ (The mean donation by Presbyterians is greater than the mean donation by Catholics)
3. **Test Statistic Calculation:**
- The test statistic is calculated using the given sample sizes, means, and standard deviations.
4. **P-value Determination:**
- The **p-value** is obtained from the t-distribution table or by using statistical software.
5. **Comparison Decision:**
- **Compare the p-value with α (0.01):**
- If the p-value is less than 0.01, we reject the null hypothesis (indicating significant evidence).
- If the p-value is greater than 0.01, we do not reject the null hypothesis (indicating insufficient evidence).
6. **Conclusion:**
- Based on the p-value and the test statistic, conclude if there is significant evidence to state that Presbyterians donate more on average than Catholics.
*How to Interpret the Results:*
- If results are **statistically significant** at α = 0.01:
- We have sufficient evidence to conclude that the population mean amount of money that Presbyterians donate is more than the population mean amount of money that Catholics donate.
- If results are **statistically insignificant** at α = 0.01:
- There is insufficient evidence to conclude that the population mean amount of money that Presbyterians donate is more than the population mean amount of
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