Which two of the following statements are false? a.The distribution of NSW household income is less skewed than the distribution of household income in Victoriab.There is no difference in the average income for households in NSW and Victoria.c.The distribution of income in NSW and Victoria exhibits different degrees of variability.d.The range of the middle 50% of household income in NSW is larger than Victoria.
Question
Which two of the following statements are false? a.The distribution of NSW household income is less skewed than the distribution of household income in Victoriab.There is no difference in the average income for households in NSW and Victoria.c.The distribution of income in NSW and Victoria exhibits different degrees of variability.d.The range of the middle 50% of household income in NSW is larger than Victoria.
Solution
Let's evaluate each statement based on the provided statistics:
a. The distribution of NSW household income is less skewed than the distribution of household income in Victoria.
This statement is false. The skewness of NSW income distribution is 1.482, which is greater than the skewness of Victoria's income distribution (1.432). Therefore, NSW's income distribution is more skewed, not less.
b. There is no difference in the average income for households in NSW and Victoria.
This statement is false. The mean income for NSW is 67510.27586, while for Victoria it is 63671. There is a difference in the average income between the two states.
c. The distribution of income in NSW and Victoria exhibits different degrees of variability.
This statement is true. The standard deviation (a measure of variability) for NSW is 16824.2, while for Victoria it is 11104.7. These are different, indicating different degrees of variability.
d. The range of the middle 50% of household income in NSW is larger than Victoria.
This statement is true. The IQR (which represents the range of the middle 50% of the data) for NSW is 21839.5, while for Victoria it is 8846.5. NSW's IQR is larger.
So, the false statements are a and b.
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