Question

Problem #8: An observational study of Alzheimer's disease (AD) obtained data from 11 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 03 Maimun 2.02 .71 77.00 79.25 87.00 92.25 93.00 4.09 12.92 54.00 56.00 5.00 82.00 89.00 21 Median Variable Alzheimers 11 0 74.51 Control N NMean SE Mean StDev Minimum 10 07.43 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? null hypothesis Problem #8(a) Problem #6(b): ? Problem #8(c): " test statistic (correct to 3 decimals) critical value (correct to 3 decimals) (A) Reject Ho since thep-value is equal to 0.1096 which is greater than.04 (B) Reject H0 since the absolue value of the answer in (b) is greater than the answer in (c). (C) Do not reject Ho since the p-value is equal to 0.0548 which is greater than.05 (D) Reject Ho since the absolue value of the answer in (b) is less than the answer in (c). (E) Do not reject Ho since the p-value is equal to 0.1096 which is greater than.05 (F) Reject Ho since the p-value is equal to 0.0548 which is greater than.05 (G) Do not reject Ho since the absolue value of the answer in (b) is greater than the answer in (c). (H) Do not reject Ho since the absolue value of the answer in (b) is less than the answer in (c)

Answer 1

(a)

The null hypothesis is

$H_{0}:\mu_{1}=\mu_{2}$

Correct option is A.

Following is the output of pooled t test :

(b)

The test statistics is:

t = 1.598

(c)

Degree of freedom: df=19

The critical value for two tailed test is: 2.093

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Correct option is H.