Questions: An economist wants to estimate the mean per capita income (in thousands of dollars) for a major city in Texas. Suppose that the mean income is known to be 52.4 for a random sample of 211 people. Assuming the population standard deviation is known to be 5.7. Construct the 80 % confidence interval for the mean per capita income for the mean per capita. Lower endpoint: Upper endpoint: Answer: How to enter your answer (opens in new window) Tables Keypad

Construct the 80% confidence interval for the mean per capita income.

Calculate the Z critical value for the 80% confidence level.

The Z critical value is calculated using the formula \( Z = \Phi^{-1}(1 - \frac{\alpha}{2}) \). For an 80% confidence level, the Z critical value is found to be \( Z = 1.2816 \).

Calculate the margin of error.

The margin of error is calculated using the formula \[ \text{Margin of Error} = \frac{Z \times \sigma}{\sqrt{n}} = \frac{1.2816 \times 5.7}{\sqrt{211}} = 0.5029. \]

Determine the lower and upper endpoints of the confidence interval.

The lower endpoint is calculated as \[ \text{Lower endpoint} = \mu - \text{Margin of Error} = 52.4 - 0.5029 = 51.8971. \] The upper endpoint is calculated as \[ \text{Upper endpoint} = \mu + \text{Margin of Error} = 52.4 + 0.5029 = 52.9029. \]

The 80% confidence interval is \(\boxed{(51.8971, 52.9029)}\).

The 80% confidence interval for the mean per capita income is \(\boxed{(51.8971, 52.9029)}\).