# ---------------------------------------------------------
# VARIABLE 1: hrs_wrked_per_weeek
# ---------------------------------------------------------
#calculate mean (point estimate)
hrs_mean <- mean(ch_pums$hrs_wrked_per_week)
#calculate sample variance
hrs_variance <- sd(ch_pums$hrs_wrked_per_week)**2
#sample size
sample_size <- nrow(ch_pums)
## ---- 90% CI ----
t_val_90 <- qt(0.95, df = sample_size - 1) # 0.90 + (0.10/2) = 0.95
hrs_ci90_lower <- hrs_mean - t_val_90 * (sqrt(hrs_variance/sample_size))
hrs_ci90_upper <- hrs_mean + t_val_90 * (sqrt(hrs_variance/sample_size))
## ---- 95% CI ----
t_val_95 <- qt(0.975, df = sample_size - 1) # 0.95 + (0.05/2) = 0.975
hrs_ci95_lower <- hrs_mean - t_val_95 * (sqrt(hrs_variance/sample_size))
hrs_ci95_upper <- hrs_mean + t_val_95 * (sqrt(hrs_variance/sample_size))
#print results
hrs_mean
## [1] 27.64611
hrs_ci90_lower; hrs_ci90_upper
## [1] 27.24431
## [1] 28.04791
hrs_ci95_lower; hrs_ci95_upper
## [1] 27.16731
## [1] 28.12491
#check using t.test() - built-in R function
t.test(ch_pums$hrs_wrked_per_week, conf.level = 0.90)
##
## One Sample t-test
##
## data: ch_pums$hrs_wrked_per_week
## t = 113.19, df = 6501, p-value < 2.2e-16
## alternative hypothesis: true mean is not equal to 0
## 90 percent confidence interval:
## 27.24431 28.04791
## sample estimates:
## mean of x
## 27.64611
t.test(ch_pums$hrs_wrked_per_week, conf.level = 0.95)
##
## One Sample t-test
##
## data: ch_pums$hrs_wrked_per_week
## t = 113.19, df = 6501, p-value < 2.2e-16
## alternative hypothesis: true mean is not equal to 0
## 95 percent confidence interval:
## 27.16731 28.12491
## sample estimates:
## mean of x
## 27.64611
# ---------------------------------------------------------
# VARIABLE 2: income
# ---------------------------------------------------------
#calculate mean (point estimate)
income_mean <- mean(ch_pums$income)
#calculate sample variance
income_variance <- sd(ch_pums$income)**2
## ---- 90% CI ----
income_ci90_lower <- income_mean - t_val_90 * (sqrt(income_variance/sample_size))
income_ci90_upper <- income_mean + t_val_90 * (sqrt(income_variance/sample_size))
## ---- 95% CI ----
income_ci95_lower <- income_mean - t_val_95 * (sqrt(income_variance/sample_size))
income_ci95_upper <- income_mean + t_val_95 * (sqrt(income_variance/sample_size))
#print results
income_mean
## [1] 69586.45
income_ci90_lower; income_ci90_upper
## [1] 67597.61
## [1] 71575.3
income_ci95_lower; income_ci95_upper
## [1] 67216.49
## [1] 71956.41
#check using t.test() - built-in R function
t.test(ch_pums$income, conf.level = 0.90)
##
## One Sample t-test
##
## data: ch_pums$income
## t = 57.559, df = 6501, p-value < 2.2e-16
## alternative hypothesis: true mean is not equal to 0
## 90 percent confidence interval:
## 67597.61 71575.30
## sample estimates:
## mean of x
## 69586.45
t.test(ch_pums$income, conf.level = 0.95)
##
## One Sample t-test
##
## data: ch_pums$income
## t = 57.559, df = 6501, p-value < 2.2e-16
## alternative hypothesis: true mean is not equal to 0
## 95 percent confidence interval:
## 67216.49 71956.41
## sample estimates:
## mean of x
## 69586.45