Question

(1 point) Alzheimer's disease is a progressive disease of the brain. An article published in 2006 was critical of the methodologt used in studies of Alzheimer's treatments conducted prior to 2006. In a random sample of n=26 Alzheimer's studies, the quality of the methodology measured on the Wong scale with scores ranging from 9 (low quality) to 27 (high quality) for each study. The data is provided below.

x=c(19,14,15,11,19,10,14,26,18,19,10,23,23,27,21,13,17,21,23,24,16,21,10,13,24,20);

A) Find a 89% confidence interval for the mean quality of studies on the treatment of Alzheimer's disease, assuming the data is NORMALLY DISTRIBUTED.

_____ ≤ μ ≤ ____ use as many digits as possible

B) Correctly complete the interpretation of the 89% confidence interval you computed in A):

? the mean quality of ? is somewhere between ____ and ____ on the Wong scale.

?1 Options : From this sample of studies

All Studies

For all persons with Alzheimer's disease

?2 Options : Does not give any options

C) If you were to decrease the level of confidence used to estimate the μ , what would happen to the confidence interval you found in (A)?

A: The confidence interval would become narrower

B: The confidence interval would become wider

C: Nothing. The confidence interval would be the same

Answer 1

using R

we have

> x=c(19,14,15,11,19,10,14,26,18,19,10,23,23,27,21,13,17,21,23,24,16,21,10,13,24,20)
> t.test(x,alternative = c("two.sided") ,conf.level = 0.89 )

   One Sample t-test

data: x
t = 17.942, df = 25, p-value = 8.616e-16
alternative hypothesis: true mean is not equal to 0
89 percent confidence interval:
16.44224 19.78853
sample estimates:
mean of x
18.11538

A)89% confidence interval is

16.44224≤ μ ≤ 19.78853

B)

From this sample of studies the mean quality of For all persons with Alzheimer's disease is somewhere between16.44224 and 19.78853 on the Wong scale.

C)

B: The confidence interval would become wider