**Educational Website Transcription:**---**Study Context:**We are examining whether the average donation by Presbyterians differs from that of Catholics during Sunday church services. 55 Presbyterian church members were observed, donating an average of $23 with a standard deviation of $6. In contrast, 41 Catholic church members donated an average of $25 with a standard deviation of $10. Our aim is to determine if there is a statistically significant difference between these two groups at the α = 0.01 level.**Analysis Steps:****a. Study Methodology:**- For this study, we should use [Select an answer]**b. Null and Alternative Hypotheses:**- **$ H_0 $ (Null Hypothesis):** - [Select an answer] [Select an answer] [Select an answer] (please enter a decimal)- **$ H_1 $ (Alternative Hypothesis):** - [Select an answer] [Select an answer] [Select an answer] (Please enter a decimal)**c. Test Statistic:**- The test statistic $ ? $ = [_______] (please show your answer to 3 decimal places)**d. p-value:**- The p-value = [_______] (Please show your answer to 4 decimal places)**e. Comparison with α:**- The p-value is [Select a comparison] α**f. Decision on Null Hypothesis:**- Based on this, we should [Select an answer] the null hypothesis.**g. Conclusion:**- **Final Statements:**1. The results are statistically significant at α = 0.01, so there is sufficient evidence to conclude that the population mean amount of money that Presbyterians donate is a different amount of money compared to the population mean amount of money that Catholics donate.2. The results are statistically insignificant at α = 0.01, so there is statistically significant evidence to conclude that the population mean amount of money that Presbyterians donate is equal to the population mean amount of money that Catholics donate.3. The results are statistically insignificant at α = 0.01, so there is insufficient evidence to conclude that the population mean amount of money that Presbyterians donate is a different amount of money compared to the population mean amount of money that Catholics donate.4. The results are statistically significant at α = 0.01, so there is sufficient evidence to

Hello! As you have posted more than 3 sub parts, we are answering the first 3 sub-parts. In case you require the unanswered parts also, kindly re-post that parts separately. a) In the given situation, the average Prebysterian donate a different amount of money compared to the average Catholic in church on Sundays. That is, the testing is based on comparing two means. Hence, we can use two sample t test. b) Null Hypothesis: H0:μ1=μ2 Alternative Hypothesis: H1:μ1≠μ2 c) Given information: n1=55x¯1=23s1=6n2=41x¯2=25s2=10 Consider, s2=n1-1s12+n2-1s22n1+n2-2 =55-162+41-110255+41-2 =63.234 t=x¯1-x¯2s21n1+1n2 =23-2563.234155+141 =-1.219