The herb ginkgo biloba is commonly used as a treatment to prevent dementia. In a

Question

The herb ginkgo biloba is commonly used as a treatment to prevent dementia. In a study of the effectiveness of this treatment, 1127 elderly subjects were given ginkgo and 1100 elderly subjects were given a placebo. Among those in the ginkgo treatment group, 113 later developed dementia, and among those in the placebo group, 132 later developed dementia. We want to use a 0.05 significance level to test the claim that ginkgo is effective in preventing dementia.

a) Determine the critical value.
b) Determine the test statistic.
c) Decide whether or not we reject or fail to reject the null hypothesis.
d) State whether or not there was sufficient evidence to support the claim.
e) Construct the confidence interval about the difference between the two proportions.
    Write the confidence interval as (LowerValue, HigherValue)

critical value =

test statistic =

[Select Decision]We reject the null hypothesisWe fail to reject the null hypothesisWe accept the alternate hypothesis

[Select Conclusion]With a 95% level of confidence, we can say ginkgo is effective in preventing dementia.There is not enough evidence to suggest ginkgo is effective in preventing dementia.

Confidence Interval about p1-p2:

Explanation / Answer

Null Hypothesis : There is no significant positive effect of using gingko in dementia. pgingko = pplacebo

ALternative Hypothesis : There is significane positive effect of using gingko in dementia . pgingko < pplacebo

(a) Determine the critical value

For left tailed Test at alpha = 0.05

Zcritical = - 1.645

b) Test Statistic:

p1 = 113/1127 = 0.100

p2 = 132/1100 = 0.12

so pooled estimate p* = (113 + 132)/ (1127+ 1100) = 0.1100

Standard Error SE= sqrt [ p* (1-p*) (1/n1 + 1/n2 )] = sqrt [ 0.11 * 0.89 * (1/1100 + 1/1127)] = 0.01326

Test Statistic

Z = (p1 - p2 )/ SE = ( 0.10 - 0.12)/ 0.01326 = - 1.5082

(c) As Z < Zcritical so we cannot reject the null hypothesis

(d) THere is no suffficient evidence to support the claim that the given drug is effective.

(e) confidence interval on differencebetween two proportions.

95 % CI = (p1 - p2) +- Z* SE0 = ( 0.12 - 0.10) +- 1.96 * 0.01326 = 0.02 +- 0.026

Lower value = -0.006

Upper value = 0.046

as the interval contain value of 0 so With a 95% level of confidence, we can say that ginkgo is not effective in preventing dementia.

for alpha

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.