Question

An observational study of Alzheimer's disease (AD) obtained data from 10 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 Minitab Output below.

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Descriptive Statistics: Alzheimers, Control

Variable	N	N*	Mean	SE Mean	StDev	Minimum	Q1	Median	Q3	Maximum
Alzheimers	10	0	75.90	2.08	6.59	77.00	79.25	87.00	92.25	93.00
Control	7	0	67.73	4.88	12.91	54.00	56.00	65.00	82.00	89.00

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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 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) H₀ : μ₁ > μ₂ (B) H₀ : μ₁ ≥ μ₂ (C) H₀ : μ₁ ≤ μ₂ (D) H₀ : μ₁ = μ₂ (E) H₀ : μ₁ ≠ μ₂ (F) H₀ : μ₁ < μ₂

Problem #6(a):  

Select A B C D E F

null hypothesis

Problem #6(b):

test statistic (correct to 3 decimals)

Problem #6(c):

critical value (correct to 3 decimals)

(A) Do not reject H₀ since the p-value is equal to 0.0427 which is less than .05.   (B) Reject H₀ since the absolue value of the answer in (b) is less than the answer in (c).   (C) Do not reject H₀ since the absolue value of the answer in (b) is less than the answer in (c).   (D) Reject H₀ since the p-value is equal to 0.0427 which is less than .05.   (E) Do not reject H₀ since the absolue value of the answer in (b) is greater than the answer in (c).   (F) Reject H₀ since the p-value is equal to 0.0854 which is greater than .05.   (G) Do not reject H₀ since the p-value is equal to 0.0854 which is greater than .05.   (H) Reject H₀ since the absolue value of the answer in (b) is greater than the answer in (c).  

Answer 1

a)

Ho:μ1=μ2

b)

test stat t =(x1-x2-Δo)/Se =

1.540

c)

for 0.05 level ,two tail test &6 df, critical t=

2.447

d)

(C) Do not reject H₀ since the absolute value of the answer in (b) is less than the answer in (c).