Income by Age. The U.S. Census Bureau collects information on the incomes of employed persons and publishes the results in Historical Income Tables. Independent simple random samples of $100\mathrm{cm}-$ ployed persons in each of four age groups gave the data on annual income, in thousands of dollars, presented on the WeissStats site.

The U.S. Census Bureau collects information on the incomes of employed persons and publishes the results in Historical Income Tables.

The MINITAB would be used to generate the normal probability plots and sample standard deviations.

Age $25-34$ (probability plot)

The MINITAB process includes the following steps:

- Select the Graph tab first, then Probability plot.

- In the second step, select Single and then OK.

- In the third step, select Graph variables and enter columns $25-34$, then click Ok.

Minitab's output would be as follows if you followed the procedures above:

Age $35-44$: Probability Graph

The MINITAB output is as follows: Only at step three should you enter columns $35-44$in the graph variables, then click the Ok tab.

Age $45-54$: Probability Graph

The MINITAB output is as follows: Only at step $3$should you enter columns $45-54$in the graph variables, then click the Ok tab.

Age $55-64$: Probability Graph

The MINITAB output is as follows: Only at step $3$should you enter column $55-64$in the graph variables, then click the Ok tab.

The U.S. Census Bureau collects information on the incomes of employed persons and publishes the results in Historical Income Tables.

The next step is to create a residual plot for each of the probability plots:

To obtain residual probability plots, follow the procedures below:

The first step is to decide whether to use Stat, Anova, or One-way. After that, enter the Income column.

The next step is to open the factor and then enter the Age column before clicking OK.

The following is the output of the Normal Probability plot:

Residual as an output (response is Income).

The output for Residual vs fits

The U.S. Census Bureau collects information on the incomes of employed persons and publishes the results in Historical Income Tables.

The samples to be taken are supposed to be independent of one another, and the population is assumed to be normal. The standard deviations of the population must be the same as well.

Calculate the highest to lowest standard deviation ratio as follows:

$\frac{30.62}{25.73}=1.15$

The axioms of the standard deviation are violated if this ratio is greater than 2. The assumptions have been met in this case.

The normal probability plot also yields a relatively straight line, indicating that the assumptions are met.

As a result, the ANOVA test is valid.

The U.S. Census Bureau collects information on the incomes of employed persons and publishes the results in Historical Income Tables.

We didn't get a straight line in the probability graphs, indicating the data distribution isn't regularly distributed.

They don't have a linear relationship between them.

As a result, conventional population assumptions are not met.

On this dataset, the ANOVA test isn't appropriate.

The U.S. Census Bureau collects information on the incomes of employed persons and publishes the results in Historical Income Tables.

We didn't get a straight line in the probability graphs, indicating the data distribution isn't regularly distributed.

They don't have a linear relationship between them.

As a result, conventional population assumptions are not met.

On this dataset, the ANOVA test isn't appropriate.