Questions: You measure 43 dogs' weights, and find they have a mean weight of 77 ounces. Assume the population standard deviation is 2.7 ounces. Based on this, construct a 95% confidence interval for the true population mean dog weight. Give your answers as decimals, to two places ± ounces

Solution Steps

To determine the Z critical value for a 95% confidence level, we use the formula:

\[ Z = \Phi^{-1}\left(1 - \frac{\alpha}{2}\right) \]

where \(\alpha = 0.05\). Thus, the Z critical value is:

\[ Z = 1.96 \]

The margin of error (ME) can be calculated using the formula:

\[ \text{Margin of Error} = \frac{Z \times \sigma}{\sqrt{n}} \]

Substituting the values:

\[ \text{Margin of Error} = \frac{1.96 \times 2.7}{\sqrt{43}} \approx 0.807 \]

The confidence interval (CI) is constructed using the sample mean and the margin of error:

\[ \text{CI} = \left(\bar{x} - \text{ME}, \bar{x} + \text{ME}\right) \]

Substituting the values:

\[ \text{CI} = \left(77 - 0.807, 77 + 0.807\right) = (76.193, 77.807) \]

Final Answer