Answer:
[tex]\{58198.2573,58239.7427\}[/tex]
Step-by-step explanation:
We assume that the following conditions are true before constructing the confidence interval:
Assumption #1: Random Sampling.
Assumption #2: Independence.
Assumption #3: Large Sample.
Assumption #4: The 10% Condition (sample size is no bigger than 10% of population
Assumption #5: The Success / Failure Condition.
Assumption #6: Homogeneity of Variances.
A 95% confidence level correlates to a critical value of [tex]z^*=1.96[/tex], hence:
[tex]\displaystyle CI=\bar{x}\pm z^*\biggr(\frac{s}{\sqrt{n}}\biggr)\\\\CI=58219\pm 1.96\biggr(\frac{56}{\sqrt{28}}\biggr)\\\\CI=58219\pm20.7427\\\\CI=\{58198.2573,58239.7427\}[/tex]
Therefore, we are 95% confident that the true mean of the average yearly income for a married couple living in city C is between $58,198.2573 and $58,239.7427
