Answer:
The true estimate of the average annual income of all 700 families living in a four square block section lies within the 92% confidence interval below
[tex] 34854.3 < \mu < 35 745.7[/tex]
Step-by-step explanation:
From the question we are told that
The sample size is n = 50
The sample mean is [tex]\= x = \$ 35300[/tex]
The population standard deviation is [tex]\sigma = \$ 1800[/tex]
From the question we are told the confidence level is 92% , hence the level of significance is
[tex]\alpha = (100 - 92 ) \%[/tex]
=> [tex]\alpha = 0.08[/tex]
Generally from the normal distribution table the critical value of [tex]\frac{\alpha }{2}[/tex] is
[tex]Z_{\frac{\alpha }{2} } = 1.751 [/tex]
Generally the margin of error is mathematically represented as
[tex]E = Z_{\frac{\alpha }{2} } * \frac{\sigma }{\sqrt{n} }[/tex]
=> [tex]E = 1.751 * \frac{1800 }{\sqrt{50} }[/tex]
=> [tex]E = 445.7 [/tex]
Generally 92% confidence interval is mathematically represented as
[tex]\= x -E < \mu < \=x +E[/tex]
=> [tex] 35 300 -445.7 < \mu < 35 300 + 445.7[/tex]
=> [tex] 34854.3 < \mu < 35 745.7[/tex]
So the true estimate of the average annual income of all 700 families living in a four square block section lies within the 92% confidence interval