Question

Forbes gave the following data about percentage return on capital for some stocks: 1.9, 2.6, 1.8, 2.6, 2.1, 4.2, 0.6, 0.9, 1.7, 3.4, 2.8, 3.1, 1.0, 0.7, 4.2, 3.2, 4.7, 1.6 (percentage return on capital is normally distributed with s = 1.244%)

Find (round to nearest hundredths):

1. The 98% confidence intervals for the population mean _________________.
2. The 85% confidence intervals for the population mean _________________.
3. How many more (than the original 18) would they need to sample to be 96% sure to be within 0.5 of the population mean? ______________.

Answer 1

a. The 98% confidence intervals for the population mean: (1.64%,3.15%)

R code:

x=c(1.9, 2.6, 1.8, 2.6, 2.1, 4.2, 0.6, 0.9, 1.7, 3.4, 2.8, 3.1, 1.0, 0.7, 4.2,
3.2, 4.7, 1.6)
m=mean(x)
s=sd(x)
n=length(x)
alpha=1-0.98
LB=m-qt(1-alpha/2,n-1)*s/sqrt(n)
UB=m+qt(1-alpha/2,n-1)*s/sqrt(n)
round(LB,2)
round(UB,2)

b. The 85% confidence intervals for the population mean: (1.95, 2.84).

R code:

x=c(1.9, 2.6, 1.8, 2.6, 2.1, 4.2, 0.6, 0.9, 1.7, 3.4, 2.8, 3.1, 1.0, 0.7, 4.2,
3.2, 4.7, 1.6)
m=mean(x)
s=sd(x)
n=length(x)
alpha=1-0.85
LB=m-qt(1-alpha/2,n-1)*s/sqrt(n)
UB=m+qt(1-alpha/2,n-1)*s/sqrt(n)
round(LB,2)
round(UB,2)