Question

value of the -variable Remaining time: 152:54 min:sec) Problem 2 (1 point) Alzheimer's disease is a progressive disease of the brain. An article published in 2006 was critical of the methodology used in studies of Alzheimer's treatments conducted prior to 2006. In a random sample of 28 Alzheimer's studies, the quality of the methodology was measured on the Wong scale with scores ranging from 9 flow quality) to 27 (high quality for each study. The data is provided below. data can be copied into R Studio using the following command: X=C(13,20,13,23,21,26,24,17,17,26,13,21,22,10,26,14,23,27,10,12,24,11,15,22,25,19,21,12); (a) Find a 86% confidence interval for the mean quality of studies on the treatment of Alzheimer's disease, Assuming the data is Normally distributed Hi SHS use as many digits as possible (b) Correctly complete the interpretation of the 38% confidence interval you computed in a II the mean quality of al Alzheimer's patients is somewhere between and From this sample of studies on the Wong scale lch you were to decrease the level of confidence used to estimate the what would happen to the confidence interval you found in (al? A. Nothing. The confidence interval would be the same OB. The confidence interval would become wider OC. The confidence interval would become narrower Id Cosy and paste the following code into R Studio to bootstrap the

Answer 1

Solution-A:

Rcode to get the 86% confidence interval

x <- c(13,20,13,23,21,26,24,17,17,26,13,21,22,10,
26,14,23,27,10,12,24,11,15,22,25,19,21,12)
t.test(x,conf.level = 0.86)

Output:

   One Sample t-test

data: x
t = 17.854, df = 27, p-value < 2.2e-16
alternative hypothesis: true mean is not equal to 0
86 percent confidence interval:
17.21853 20.42432
sample estimates:
mean of x
18.82143

Intreretation:

86 percent confidence interval:
17.21853 20.42432

we are 86% confidenct that the true mean quality of studies on the treatment of Alzmeirs disease lies in between

17.21853 and 20.42432

ANSWER:

17.21853 <mu<20.42432

Solution-b:

we are 86% confidenct that the true mean quality of studies on the treatment of Alzmeirs disease lies in between

17.21853 and 20.42432 on the Wong scale

Solution-c:

if we reduce to say 70

70 percent confidence interval:
17.70747 19.93539

ANSWER:

confidence interval would become narower

Solutiond:

Rcode:

library(mosaic)
RNGkind(sample.kind = "Rejection")
set.seed(6370)
B=do(1000)*mean(resample(c(13,20,13,23,21,26,24,17,17,26,13,21,22,10,
26,14,23,27,10,12,24,11,15,22,25,19,21,12))
t.test(B,conf.level = 0.86)

Output:

One Sample t-test

data: B
t = 1266.4, df = 999, p-value < 2.2e-16
alternative hypothesis: true mean is not equal to 0
86 percent confidence interval:
11.84407 11.87173
sample estimates:
mean of x
11.8579

ANSWER:

86 percent confidence interval:
11.84407 11.87173

11.84407<mu< 11.87173