Question

Problem #2: An observational study of Alzheimer's disease (AD) obtained data from 14 AD patients exhibiting moderate dementia and selected a group of 10 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 Minitab Output below. Descriptive Statistics: Alzheimers, Control Variable N N* Alzheimers 14 0 Control 10 0 Mean SE Mean StDev Minimum 01 Median Q3 Maximum 79.31 1.79 6.71 77.00 79.25 87.00 92.25 93.00 63.47 4.10 12.95 54.00 56.00 65.00 82.00 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 population variances are not 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) HO:M1 M2 (B) H: U1 = u2 (C) H: U12 U2 (D) HO:M1 < u2(E) HOM1 > U2 (F) Hui su2 Problem #2(a): Select ) null hypothesis Problem #2(b): test statistic (correct to 3 decimals) Problem #2(c): critical value (correct to 3 decimals) (A) Do not reject Ho since the p-value is equal to 0.0002 which is less than 05. (B) Do not reject H, since the p-value is equal to 0.0004 which is less than 05. (C) Reject Ho since the absolue value of the answer in (b) is less than the answer in (c). (D) Reject H, since the p-value is equal to 0.0002 which is less than .05. (E) Reject H, since the p-value is equal to 0.0004 which is less than .05. (F) Do not reject H, since the absolue value of the answer in (b) is greater than the answer in (c). (G) Do not reject Hsince the absolue value of the answer in (b) is less than the answer in (c). (H) Reject Ho since the absolue value of the answer in (b) is greater than the answer in (c). Problem #2(d): Select conclusion Just Save Submit Problem #2 for Grading

Answer 1

a)

(B) H:41 = 2 (

b)

	group 1	group 2
sample mean x =	79.310	63.470
std deviation s=	6.710	12.950
sample size n=	14	10
Point estimate =x1-x2=		15.840
std error =√(S21/n1+S22/n2)=		4.4706
test stat t =(x1-x2-Δo)/Se =		3.543

c)

deg of freedom='min(n1,n2)-1=		9
for 0.05 level ,two tail test &9 df, critical t=			2.262	from excel: t.inv(0.975,9)

d)

option H is correct