Question

Consider the following observations on a receptor binding measure (adjusted distribution volume) for a sample of 13 healthy individuals: 22, 39, 40, 42, 43, 46, 52, 58, 63, 66, 68, 70, 73.

(a)

Is it plausible that the population distribution from which this sample was selected is normal?

( yes or no) , it ( is or is not)

plausible that the population distribution is normal.

(b)

Calculate an interval for which you can be 95% confident that at least 95% of all healthy individuals in the population have adjusted distribution volumes lying between the limits of the interval. (Round your answers to three decimal places.)

(       ,          )

(c)

Predict the adjusted distribution volume of a single healthy individual by calculating a 95% prediction interval. (Round your answers to three decimal places.)

(           ,         )

How does this interval's width compare to the width of the interval calculated in part (b)?

This interval's width is ( less or greater)

than the width of the interval calculated in part (b).

Answer 1

a) yes, it is

b)

sample mean         x=	52.462
sample size             n=	13.000
sample std deviation s=	15.2786
std error sx=s/√n=	4.2375

for 95% CI; and 12 df, critical t=		2.1790
margin of error E=t*std error                            =		9.234
lower bound=sample mean-E =		43.228
Upper bound=sample mean+E=		61.695
from above 95% confidence interval for population mean =(43.228 ,61.695)

c)

std errror of mean ='s=s*√(1+1/n)=		15.855
for 95% CI; and 12 df, value of t=		2.1790
margin of error E=t*std error     =		34.5488
lower bound=sample mean-margin of error =		17.913
Upper bound=sample mean +margin of error=		87.010

95% prediction interval for population mean =(17.913 ,87.010)

This interval's width is greater than the width of the interval calculated in part (b)