Question

Suppose that the US population average household annual income is $60,000. City Officials in San Diego want to determine if the average household annual income in San Diego is different than the national average. Assume they don’t know how to conduct hypothesis testing using p-values but have collected data useful for constructing a 95% confidence interval. They provide the following for San Diego: sample mean of $70,000 and margin of error of $11,000.

a. Construct the 95% confidence interval

b. Is San Diego average income different from the national average? Use a=.05 and what you know about confidence intervals to answer this question (no p-values are required here). Justify your answer.

Answer 1

To construct a 95% confidence interval, subtract the margin of error from the sample mean to find the lower bound, and add the margin of error to the sample mean to find the upper bound. If the confidence interval does not include the national average, it can be concluded that the average household income in San Diego is different from the national average.

Step-by-step explanation:

To construct a 95% confidence interval, we can use the formula: sample mean ± margin of error. Given that the sample mean for San Diego is $70,000 and the margin of error is $11,000, the 95% confidence interval can be calculated as follows:

Lower bound = $70,000 - $11,000 = $59,000
Upper bound = $70,000 + $11,000 = $81,000

Therefore, the 95% confidence interval for the average annual household income in San Diego is $59,000 to $81,000.

To determine if the average household income in San Diego is different from the national average, we need to check if the 95% confidence interval overlaps with the national average ($60,000). If the confidence interval contains the national average, then we cannot conclude that the average income in San Diego is different from the national average. In this case, since the confidence interval of $59,000 to $81,000 does not include $60,000, we can conclude that the average household income in San Diego is different from the national average.