Problem #3: An observational study of Alzheimer's disease (AD) obtained data from 11 AD patients exhibiting moderate dementia and selected a group of 7 control individuals without AD. AD is a progressive neurodegenerative disease of the elderly and advancing age is known to be a primary risk factor in AD diagnosis. Therefore, it was crucial for the study's credibility to examine whether the ages in the AD group might be significantly different than in the control group. The ages of the subjects in years are summarized in the R. Output below. Variable Alzheimers 11 Control n Mean 76.67 sd 6.74 7 67.55 12.92 Minimum 77.00 54.00 Q1 Median Q3 Maximum 79.25 87.00 92.25 56.00 65.00 82.00 93.00 89.00 We want to test if the average age in the Alzheimer's group is significantly different than the control group. Assume that the populations are normal and that the population variances are equal. (a) What is the null hypothesis? (b) Find the value of the test statistic. (c) Find the 5% critical value. (d) What is the conclusion of the hypothesis test? (A) H₁₁₂ (B) H₁₁₂ (C) H₁₁₂ (D) Ho₁142 (E) 0:41 ≤42 (F) H0-41=42 Problem #3(a): Select Problem #3(b): Problem #3(c): Problem #3(d): null hypothesis test statistic (correct to 3 decimals) critical value (correct to 3 decimals) (A) Fail to reject Ho since the absolue value of the answer in (b) is greater than the answer in (c). (B) Fail to reject Ho since the p-value is equal to 0.0478 which is less than .05. (C) Reject Ho since the p-value is equal to 0.0239 which is less than .05. (D) Fail to reject Ho since the absolue value of the answer in (b) is less than the answer in (c). (E) Reject Ho since the p-value is equal to 0.0478 which is less than .05. (F) Reject Ho since the absolue value of the answer in (b) is less than the answer in (c). (G) Fail to reject Ho since the p-value is equal to 0.0239 which is less than .05. (H) Reject Ho since the absolue value of the answer in (b) is greater than the answer in (c). Select conclusion