Question

19. The average yearly income for 28 married couples living

in city C is $58,219. The standard deviation of the sample is
$56. Find the 95% confidence interval of the true mean.
20. The number of unhealthy days based on the AQI

Answer 1

`\{58198.2573,58239.7427\}`

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
`z^*=1.96`, hence:

`\displaystyle CI=\bar{x}\pm z^*\biggr((s)/(√(n))\biggr)\\\\CI=58219\pm 1.96\biggr((56)/(√(28))\biggr)\\\\CI=58219\pm20.7427\\\\CI=\{58198.2573,58239.7427\}`

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