Question

Speed Dating Use these female measures of male attractiveness given in Exercise 18 “Speed Dating” in Section 7-2 on page 329: 5, 8, 3, 8, 6, 10, 3, 7, 9, 8, 5, 5, 6, 8, 8, 7, 3, 5, 5, 6, 8, 7, 8, 8, 8, 7. Use the bootstrap method with 1000 bootstrap samples.

1. Construct a 99% confidence interval estimate of the population mean. Is the result dramatically different from the 99% confidence interval found in Exercise 18 in Section 7-2?
2. Construct a 95% confidence interval estimate of the population standard deviation. Is the result dramatically different from the 95% confidence interval found in Exercise 14 “Speed Dating” in Section 7-3 on page 340?

 

Answer 1

a) The 99% confidence interval estimate of the population mean is (5.549, 7.605).

Again, the 99% confidence interval estimate of the population mean using the bootstrap method with 1000 bootstrap samples is(5.615192, 7.538654). The CI results between the parametric and bootstrap do not dramatically different.

b) The 95% confidence interval estimate of the population standard deviation using the parametric method is (1.47, 2.59). Again the 95% confidence interval estimate of the population standard deviation using the bootstrap method is (1.297937, 2.236433). The CI results between the parametric and bootstrap do not dramatically different.

#### RUN IN R

> x=c(5, 8, 3, 8, 6, 10, 3, 7, 9, 8, 5, 5, 6, 8, 8, 7, 3, 5, 5, 6,
+ 8, 7, 8, 8, 8, 7)
>
>
> #######
# a) 99% confidence interval estimate of the population mean

>
> Boot_mean=function(data, nsim)
+ {
+ n=length(data)
+ BOOT=list()
+ MEAN=list()
+ SD=list()
+ for(i in 1:nsim)
+ {
+ BOOT[[i]]=sample(data, size=n, replace = TRUE)
+ MEAN[[i]]=mean(BOOT[[i]])
+ }
+ return(MEAN)
+ }
>
>
> ## Run
>
> MEAN=Boot_mean(data=x, nsim=1000)
>
> MEAN=unlist(MEAN)
> # 95% CI of MEAN
> QMEAN=quantile(MEAN, c(.005, .995))
> QMEAN
0.5% 99.5%
5.615192 7.538654

> ### b) 95% confidence interval estimate of the population standard deviation
> Boot_SD=function(data, nsim)
+ {
+ n=length(data)
+ BOOT=list()
+ SD=list()
+ for(i in 1:nsim)
+ {
+ BOOT[[i]]=sample(data, size=n, replace = TRUE)
+ SD[[i]]=sd(BOOT[[i]])
+ }
+ return(SD)
+ }
>
> ### RUN
> SD=Boot_SD(data=x, nsim=200)
>
> SD=unlist(SD)
> # 95% CI of SD
> QSD=quantile(SD, c(.025, .975))
> QSD
2.5% 97.5%
1.297937 2.236433

###

x=c(5, 8, 3, 8, 6, 10, 3, 7, 9, 8, 5, 5, 6, 8, 8, 7, 3, 5, 5, 6,
8, 7, 8, 8, 8, 7)

#######
# a) 99% confidence interval estimate of the population mean

Boot_mean=function(data, nsim)
{
n=length(data)
BOOT=list()
MEAN=list()
SD=list()
for(i in 1:nsim)
{
BOOT[[i]]=sample(data, size=n, replace = TRUE)
MEAN[[i]]=mean(BOOT[[i]])
}
return(MEAN)
}

## Run

MEAN=Boot_mean(data=x, nsim=1000)

MEAN=unlist(MEAN)
# 95% CI of MEAN
QMEAN=quantile(MEAN, c(.005, .995))
QMEAN

####
### b) 95% confidence interval estimate of the population standard deviation
Boot_SD=function(data, nsim)
{
n=length(data)
BOOT=list()
SD=list()
for(i in 1:nsim)
{
BOOT[[i]]=sample(data, size=n, replace = TRUE)
SD[[i]]=sd(BOOT[[i]])
}
return(SD)
}

### RUN
SD=Boot_SD(data=x, nsim=200)

SD=unlist(SD)
# 95% CI of SD
QSD=quantile(SD, c(.025, .975))
QSD