Question

Make a bar chart showing the proportions of gender of your sample. Find US national proportions from a current reputable source on line. Make a table to compare your data set with national proportions. Is your data set close to national proportions or does it diverge? Why is this a problem (or not)? You need not do any mathematical analysis, just look at the proportions and comment on how adequate your data set replicates (or does not) national proportions. Be sure to include your source.

Make a bar chart showing the proportions of gender of your sample. Find US national proportions from a current reputable source on line. Make a table to compare your data set with national proportions. Is your data set close to national proportions or does it diverge? Why is this a problem (or not)? You need not do any mathematical analysis, just look at the proportions and comment on how adequate your data set replicates (or does not) national proportions. Be sure to include 8. your source.

Answer 1

We are asked to compare the proportion of gender in the sample.

The number of Females in the sample = 109

Number of males in the sample = 69

the total sample size = 109+69= 178

The proportion of females (in the sample) = 109/178=0.61

The proportion of males (in the sample) = 69/178=0.39

The bar chart showing the proportion of gender of your sample is

The proportions of gender in the sample 0.70 0.60 0.50 0.40 0.61 0.39 2 0.30 0.20 0.10 0.00 Males Females Gender

Next we are asked to make a table to compare the sample with the national proportions. The following table shows the proportions

We create this table for the sample

	Sample
	Male	Female	Total
Under 18 years	1	2	3
18 to 24 years	62	103	165
25 to 44 years	5	4	9
45 to 64 years	1	0	1
Total	69	109	178

We divide all the values by 178 to get the sample proportion of each of the age group, gender combination

	Sample Proportion
	Male	Female	Total
Under 18 years	0.01	0.01	0.02
18 to 24 years	0.35	0.58	0.93
25 to 44 years	0.03	0.02	0.05
45 to 64 years	0.01	0.00	0.01
Total	0.39	0.61	1.00

Similarly we get the table for national numbers

	National
	Male	Female	Total
Under 18 years	37609	36033	73642
18 to 24 years	15819	15025	30844
25 to 44 years	42753	42395	85148
45 to 64 years	41105	43145	84250
Total	137286	136598	273884

Divide each of these values by 273884 and get

	National Proportion
	Male	Female	Total
Under 18 years	0.14	0.13	0.27
18 to 24 years	0.06	0.05	0.11
25 to 44 years	0.16	0.15	0.31
45 to 64 years	0.15	0.16	0.31
Total	0.50	0.50	1.00

First we compare the overall proportions of gender (The column proportions)

In the sample the proportion of males is 0.39 and females is 0.61, in comparison the national proportion of males and females in 0.50. Hence the sample is skewed towards females where as the data is equally distributed among the 2 genders in the national data.

Next we compare the overall proportions in each age group. (The row totals)

We can see that 93% of the sample proportion is in the 18 to 24 year bracket. In comparison only 11% of the  national data belongs to 18 to 24 years. Hence the sample is highly skewed towards the 18 to 24 year olds.

Hence we can say that our sample is skewed towards females and towards 18 to 24 year olds. Hence the sample does not adequately represent the national proportions.