Estimate the mean wage & proportion of white male/female professionals living in the north
Descriptive statistics for both male and female wages
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 124 5.73 3.36 4.68 5.19 2.32 1.5 21.86 20.36 1.91 4.78 0.3Descriptive statistics for female wages
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 63 4.4 2.1 3.75 4.1 1.25 1.5 14.58 13.08 2.15 6.94 0.26Descriptive statistics for male wages
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 61 7.11 3.85 6.25 6.57 3.34 2 21.86 19.86 1.49 2.67 0.49## data$female: Female
## wage female
## Min. : 1.500 Female:63
## 1st Qu.: 3.025 Male : 0
## Median : 3.750
## Mean : 4.396
## 3rd Qu.: 5.150
## Max. :14.580
## ------------------------------------------------------------
## data$female: Male
## wage female
## Min. : 2.000 Female: 0
## 1st Qu.: 4.500 Male :61
## Median : 6.250
## Mean : 7.107
## 3rd Qu.: 8.750
## Max. :21.860Observations for 63 females: - Minimal wage -> 1.5; - Maximal wage -> 14.58; - Wages mean -> 4.4; - Wages median -> 3.75; - Wages standard deviation -> 2.1
Observations for 61 males: - Minimal wage -> 2; - Maximal wage -> 21.86; - Wages mean -> 7.11; - Wages median -> 6.25; - Wages standard deviation -> 3.85
Boxplot with male and female wages
As it is displayed, male wages are significantly better. Male wages have a bigger: range, mean, median and lower standard deviation.
Male and female quantile-quantile plots are right skewed.
Female wages density function
Female wages are mostly distributed between 1.5 and 7.5
Female wages density function
Male wages are mostly distributed between 2 and 10
Calculated mean and confidence interval of a random sample of 20 female wages
## [1] 3.561031 4.598970We are in 95% confident that the true female wages lies between the above two values.
Calculated mean and confidence interval of a random sample of 20 male wages
## [1] 6.404458 8.336543We are in 95% confident that the true female wages lies between the above two values.
Estimated proportion interval in a random sample of 20 females who have wages lower than the population mean
## [1] 0.0430944 0.4100154We are in 95% confident that the true proportion of females who have wages lower than the population mean lies between the above two values.
Calculated sample size needed to gain 0.1 error
##
## sample.size.prop object: Sample size for proportion estimate
## With finite population correction: N=63, precision e=0.1 and expected proportion P=0.4996
##
## Sample size needed: 39The minimum sample size to gain 0.1 error is equal to 39.