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Asked Jun 9, 2019
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A research group claims that 20% of patients with dementia never develop full Alzheimer's. In a simple random sample of 1,000 patients with dementia, 150 report that they never develop full Alzheimer's. Test the claim of the research group using a 5% significance level.

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Expert Answer

Step 1

According to the given question, to test the hypothesis that the research group claims that 20% of patients with dementia never develop full Alzheimer's. In a simple random sample of 1,000 patients with dementia, 150 report that they never develop full Alzheimer's. To test the claim of the research group using a 5% significance level we define the hypothesis as follows:

Null hypothesis as: H0: 20% of patients with dementia never develop full Alzheimer's

Against the alternative hypothesis as;

Ha: 20% of patients with dementia develop full Alzheimer's

In order to test this hypothesis we Z test statistics for single proportion as follows:

Step 2
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Test Statistics: The hypothesis testis definedas; Null hypothesis: Ho p 0.20 Altenative hypothesis as: Ha p 0.20 The test statistics is defined as: Z pl-p) 77 Where n is the sample of 1,000 patients with dementia, 150 report that they never develop full Alzheim wwwww Hence 150 p 0.15 1000 n Z= -p p(1-p) 0.15-020 Z 0.20(1-0.20) 1000 Z =-3.953

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Step 3
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Decision about the null hypothesis Since it is observed that Z=3.953> Zs = 1.96 And also according o the P value approaches P-value 0.0001a= 0.05 Hence the null hypothesis is rejected

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Math

Statistics

Hypothesis Testing

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