Question

An observational study of Alzheimer's disease (AD) obtained data from 7 AD patients exhibiting moderate dementia and selected a group of 6 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* Mean SE Mean StDev Minimum Q1 Median Q3 Maximum Alzheimers 7 0 75.63 2.53 6.70 77.00 79.25 87.00 92.25 93.00 Control 6 0 67.49 5.23 12.81 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 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) was u1=u2 was correct

B) 1.401 was INCORRECT

Answer 1

(a)

H0: Null Hypothesis:

(b)

n1 = 7

n2 = 6

1 = 75.63

2= 67.49

s1 = 6.70

s2 = 12.84

= 0.05

Pooled Standard Deviation is given by:

Test Statistic is given by:

(c)

df = 7 + 6 - 2 = 11

= 0.05

From Table, critical values of t = 2.201

(d)

Since calculated value of t = 1.4673 is less than critical value of t = 2.201, the difference is not significant. Fail to reject null hypothesis.

Conclusion:
Th data do not support the claim that the average age in the Alzheimer's group is significantly different than the control group.