Stat 382: Exam 1, Problem 2

2/13/15, 8:00pm: Changed document title, and fixed non-computational error that displayed collective BMI mean instead of the mean for the subset of females.

First, we load the data into R and preview the data.

data = read.csv('/Users/Max/Desktop/Exam1.csv')
head(data)

##    BMI FEMALE
## 1 27.7      1
## 2 23.0      1
## 3 29.1      0
## 4 29.1      1
## 5 22.9      1
## 6 32.7      1

Compute the mean, standard deviation, 5th, 25th, median, 75th, 95th quantile, as well as 95% confidence interval of the mean of BMI.

bmi_mean = mean(data$BMI); bmi_mean

## [1] 31.76547

bmi_sd = sd(data$BMI); bmi_sd

## [1] 7.259151

bmi_quantile = quantile(data$BMI, probs = c(.05, .25, .5, .75, .95))
bmi_quantile

##     5%    25%    50%    75%    95% 
## 22.000 26.600 30.700 35.700 45.605

error <- qt(0.975,df=length(data$BMI)-1)*sd(data$BMI)/sqrt(length(data$BMI))
error

## [1] 0.3077321

conf_interval = bmi_mean + c(-1,1)*error
conf_interval

## [1] 31.45774 32.07320

Compute 90% confidence interval of the proportion of female.

fem_data = data[data$FEMALE==1,]
fem_bmi_mean = mean(fem_data$BMI); fem_bmi_mean

## [1] 32.50974

fem_error <- qt(0.95,df=length(fem_data$BMI)-1)*sd(fem_data$BMI)/sqrt(length(fem_data$BMI))
fem_error

## [1] 0.3750694

fem_conf_interval = fem_bmi_mean + c(-1,1)*fem_error
fem_conf_interval

## [1] 32.13467 32.88481