Answer:
a
The 90% confidence interval is [tex]52561.13 < \mu < 57540.8[/tex]
b
Confidence interval for the population men between $52561.13 up to $57540.8
Step-by-step explanation:
From the question we are told that
The sample size is [tex]n = 25[/tex]
The sample mean is [tex]\= x = \$ 55,051[/tex]
The standard deviation is [tex]\sigma = \$ 7,568[/tex]
Given that the confidence level is 90% then the level of confidence is mathematically represented as
[tex]\alpha = 100 -90[/tex]
[tex]\alpha = 10\%[/tex]
[tex]\alpha = 0.10[/tex]
Next we obtain the critical value of [tex]\frac{\alpha }{2}[/tex] from the normal distribution table the values is
[tex]Z_{\frac{\alpha }{2} } = 1.645[/tex]
Generally the margin of error is mathematically represented as
[tex]E = Z_{\frac{ \alpha }{2} } * \frac{ \sigma }{\sqrt{n} }[/tex]
substituting values
[tex]E = 1.645 * \frac{ 7568}{ \sqrt{ 25} }[/tex]
[tex]E = 2489.9[/tex]
The 90% confidence interval is mathematically evaluated as
[tex]\= x -E < \mu < \= x +E[/tex]
substituting values
[tex]55051 - 2489.8 < \mu < 55051 + 2489.8[/tex]
[tex]52561.13 < \mu < 57540.8[/tex]
