Final answer:
To construct a 95% confidence interval for estimating the population mean, we can use the formula: Confidence Interval = Sample Mean ± (Critical Value * Standard Error). The 95% confidence interval for estimating the population mean μ is approximately $67,965.35 to $78,034.65.
Step-by-step explanation:
To construct a 95% confidence interval for estimating the population mean, we can use the formula:
Confidence Interval = Sample Mean ± (Critical Value * Standard Error)
Given that the sample mean is $73,000, the standard deviation is $18,004.7, and we want a 95% confidence level, we need to determine the critical value and the standard error.
The critical value can be found using a Z-table, since we have a large sample (n > 30). For a 95% confidence level, the critical value is approximately 1.96.
The standard error can be calculated using the formula: Standard Error = σ / √n, where σ is the standard deviation and n is the sample size. In this case, the standard error is $18,004.7 / √35 = $3,050.96.
Plugging in the values, we can calculate the confidence interval:
Confidence Interval = $73,000 ± (1.96 * $3,050.96)
Therefore, the 95% confidence interval for estimating the population mean μ is approximately $67,965.35 to $78,034.65.