Question

Ginkgo for Dementia The herb ginkgo biloba is commonly used as a treatment to prevent dementia. In a study of the effectiveness of

this treatment, 1545 elderly subjects were given ginkgo and 1524 elderly subjects were given a placebo. Among those in the ginkgo

treatment group, 246 later developed dementia, and among those in the placebo group, 277 later developed dementia. We want to

use a 0.01 significance level to test the claim that ginkgo is effective in preventing dementia. Test the claim using a hypothesis test.

Given test Statistic z = -1.66

Write Hypothesis and Critical Value, do you Support or reject the claim.

Answer 1

i) 2.58

ii) We reject the claim

Explanation:

The number of subjects in the ginkgo treatment group, n₁ = 1,545

The number of subjects in the placebo group, n₂ = 1,524

The number that developed dementia in the ginkgo group = 246

The number that developed dementia in the placebo group = 277

The proportion that developed dementia in the ginkgo group,
`\hat{p}_1` = 246/1,545 = 82/515

The proportion that developed dementia in the placebo group,
`\hat{p}_2` = 277/1,524

The null hypothesis is H₀;
`\hat{p}_1` =
`\hat{p}_2`

The alternative hypothesis is Hₐ;
`\hat{p}_1` ≠
`\hat{p}_2`

The z-test statistic is given as follows;

`Z=\frac{\hat{p}_1-\hat{p}_2}{\sqrt{\hat{p} \cdot (1-\hat{p}) \cdot \left ((1)/(n_(1))+(1)/(n_(2)) \right )}}`

Therefore, we get;

`Z=\frac{(82)/(515) -(277)/(1,524) }{\sqrt{\left (((82)/(515) * \left(1 - (82)/(515) \right) )/(1,545)+((277)/(1,524) * \left (1 - (277)/(1,524) \right))/(1,524) \right )}} \approx -1.66`

From the the p-value at z ≈ -1.66 is p = 0.04846.

i) The z-Critical at 0.01 significant level is 2.58

ii) Given that the p-value, 0.04846, is larger than the significant level, 0.01, the p-value is not significant, and we fail to reject the null hypothesis

There is sufficient statistical evidence to suggest that there is no difference in the proportion of the subject on the ginkgo treatment and the proportion of the subject on the placebo treatment that have dementia, we therefore reject the claim that the herb ginkgo biloba is effective for the treatment of dementia.