## Answers

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

.