Thank you for the clarification. Let's recalculate the 90% confidence interval for the mean pulse rate of adult females using the t-distribution.

Steps for Calculation

1. Calculate the sample mean ($\bar{x}$) and sample standard deviation ($s$) for the female pulse rates.
2. Determine the critical t-value ($t_{\alpha/2}$) for a 90% confidence interval with $df = n - 1$.
3. Compute the margin of error ($E$).
4. Construct the confidence interval.

Step 1: Calculate the Sample Mean and Sample Standard Deviation

Pulse rates for females: 79, 87, 85, 81, 80, 77, 76, 86, 74, 95, 90, 64, 89, 92, 66, 72, 62, 84, 65, 64, 60, 74, 55, 68, 67, 67, 57, 77

Calculate the Mean ($\bar{x}$):

$\bar{x} = \frac{\sum x_i}{n} = \frac{2096}{28} = 74.9$

Calculate the Sample Standard Deviation ($s$):

$s = \sqrt{\frac{\sum (x_i - \bar{x})^2}{n-1}} \approx 10.2$

Step 2: Determine the Critical t-Value

For a 90% confidence interval with $df = n - 1 = 27$, the critical t-value ($t_{\alpha/2}$) can be found using a t-table or a calculator. For 27 degrees of freedom and a 90% confidence level, $t_{0.05} \approx 1.703$.

Step 3: Compute the Margin of Error

$E = t_{\alpha/2} \cdot \frac{s}{\sqrt{n}} = 1.703 \cdot \frac{10.2}{\sqrt{28}} \approx 3.3$

Step 4: Construct the Confidence Interval

$\bar{x} - E < \mu < \bar{x} + E$ $74.9 - 3.3 < \mu < 74.9 + 3.3$ $71.6 < \mu < 78.2$

Final Answer

The 90% confidence interval for the mean pulse rate for adult females is:

$71.6 \text{ bpm} < \mu < 78.2 \text{ bpm}$

Would you like more details or have any questions? Here are five related questions you might want to explore:

1. How do you calculate a confidence interval for a population proportion?
2. What is the difference between a z-distribution and a t-distribution?
3. How do you determine the sample size needed for a specific margin of error?
4. What assumptions are necessary for constructing confidence intervals?
5. How do you interpret confidence intervals in hypothesis testing?

Tip: Always ensure the sample data is randomly selected and representative of the population to make valid inferences.