part 5

One sample T confidence interval: μ : Mean of variable

90% confidence interval results:

Variable Sample Mean Std. Err. DF L. Limit U. Limit

Overall Average 59842.692 1613.8082 51 57139.104 62546.281

White 64430.885 2097.8149 51 60916.447 67945.322

Black/African American

40358.596 1286.4605 51 38203.408 42513.784

One sample T confidence interval: μ : Mean of variable

98% confidence interval results:

Variable Sample Mean Std. Err. DF L. Limit U. Limit

Overall Average 59842.692 1613.8082 51 55966.781 63718.604

Black/African American

40358.596 1286.4605 51 37268.881 43448.311

White 64430.885 2097.8149 51 59392.526 69469.243

Interpretation Sentences:

1. We are 90% confident that the average income for overall individuals is

between $57,139.104 and $62,546.281.

2. We are 90% confident that the average income for Black/African American

individuals is between $60,916.447 and $67,945.322.

3. We are 90% confident that the average income for white individuals is

between $38,203.408 and $42,513.784.

4. We are 98% confident that the average income for overall individuals is

between $55,966.781 and $63,718.604.

5. We are 98% confident that the average income for Black/African American

individuals lies between $37,268.881 and $43,448.311.

6. We are 98% confident that the average income for White individuals lies

between $59,392.526 and $69,469.243.

Discussion on Confidence Levels:

As the confidence level increases, strides from 90% to 98%, variability of confidence

intervals also grows. Such an increase in the CI length demonstrates that the collected data

provide a higher level of accuracy in estimating the population parameter. This indicates

that, as such confidence levels increase, the flux of possible population means gets larger

and the area of the range exceeds other values.