Estimate the mean wage & proportion of married and unmarried female professionals living in the west

Table containing the information about wages of all females living in west

##    vars  n mean   sd median trimmed  mad  min max range skew kurtosis   se
## X1    1 48 5.07 2.58    4.5    4.74 2.28 0.53  15 14.47 1.47     2.98 0.37

Table containing the information about wages of married females living in west

##    vars  n mean  sd median trimmed  mad  min max range skew kurtosis  se
## X1    1 23 5.07 2.9   4.27    4.54 1.99 2.65  15 12.35 1.87     3.49 0.6

Table contaning the information about wages of all unmarried living in west

##    vars  n mean  sd median trimmed  mad  min   max range skew kurtosis   se
## X1    1 25 5.06 2.3      5    4.92 2.08 0.53 10.63  10.1 0.51    -0.02 0.46

As it can be seen from the table, the mean wage is similar in all cases, however median for married females (4.27) is lower than in case of unmarried females (5).

The minimum and maximum wages differ quite significantly. The minimum wage for married women is 2.65 and maximum is 15, while minimum wage for unmarried women is only 0.53 and maximum is 10.63.

In case of married females, the skewness is 1.87 and for unmarried it is 0.51, hence both distributions are right skewed, but the bigger part of married females is at the left (comparing to unmarried). The kurtosis calculated for married females is 3.49, hence the distribution is leptokurtic. Since kurtosis for unmarried females is -0.02 it is almost normal, but tends to be platykurtic (because of the minus sign).

Boxplot with wages of married and unmarried females

On the boxplot with wages of married and unmarried females it can be observed, that the IQR for both married and unmarried women is similar, however median for not married is higher (as it was stated from the table). Outliers appear in both cases, however in case of married females the number is especially high: 15. At the same time, the range of most wages is lower for married than for unmarried.

Denisty plot showing distribution of wages in case of married and unmarried women

On the density plot showing can be observed what was stated before: that both distributions was right skewed, distribution of married females is leptokurtic and distibution of unmarried: normal/platykurtic. The skewness tell as that in both cases mean is grater than the median (what was also confirmed by result from the table).

#Histogram showing how wages of married and unmarried females are distributed

#Plot showing relationship between education, earnings and being married

##             (Intercept) wage1$marriedNotmarried        wage1$femaleMale 
##                5.225507               -1.339481                2.294403

Mean interval estimation

of the wages of all females in the west

## [1] 4.337703 5.796880
## [1] 3.889316 6.260249
## [1] 3.923341 6.197459

This result shows that there is 95% of confidence that the actual mean of wages of females from north lies between 4.337703 and 5.796880. From the table we know that the mean is equal to 5.07, hence it lies between this two values.

Confidence mean intervals (95% confidence level) for married and not married are as follows: married: (3.889316, 6.260249) not married: (3.923341, 6.197459)

Proportion interval estimation

of married females living in the west

## [1] 0.4791667
## [1] 0.3378387 0.6204946
## 
## sample.size.prop object: Sample size for proportion estimate
## With finite population correction: N=48, precision e=0.1 and expected proportion P=0.4996
## 
## Sample size needed: 33

The proportion of married female living in the west is 0.4791667. The result showed that there is 95% confidence that the proportion is between 0.3378387 and 0.6204946.

Minimum sample size to have 0.1 error and 95% confidence level is 33. The sample of all females in the west is of size 48.