To construct a 90% confidence interval for the mean pulse rate of adult females, I will proceed as follows:

1. Calculate the Sample Mean ($\bar{x}$) for female pulse rates.
2. Calculate the Sample Standard Deviation ($s$) for female pulse rates.
3. Use the Confidence Interval Formula for the mean of a normally distributed population, which for a 90% confidence interval is: $\bar{x} \pm z \cdot \frac{s}{\sqrt{n}}$ where $z$ is the critical value for a 90% confidence level, approximately 1.645.

I'll extract the female pulse rate data from the image and perform these calculations. Let me first transcribe the female pulse rate dataTo construct a 90% confidence interval for the mean pulse rate of adult females, I will proceed as follows:

1. Calculate the Sample Mean ($\bar{x}$) for female pulse rates.
2. Calculate the Sample Standard Deviation ($s$) for female pulse rates.
3. Use the Confidence Interval Formula for the mean of a normally distributed population, which for a 90% confidence interval is: $\bar{x} \pm z \cdot \frac{s}{\sqrt{n}}$ where $z$ is the critical value for a 90% confidence level, approximately 1.645.

I'll extract the female pulse rate data from the image and perform these calculations. Let me first transcribe the female pulse rate

Female Pulse Rate Data

• Female Pulse Rates (bpm): $79, 83, 95, 82, 60, 72, 69, 72, 53, 85, 81, 91, 79, 86, 83, 93, 71, 91, 56, 93, 37, 68, 94, 68, 81, 73, 74, 82, 68, 73, 54, 66, 68, 98, 62, 81, 62, 77, 64, 76$

I will now calculate the required statistics and construct the confidence interval.The 90% confidence interval for the mean pulse rate of adult females is approximately:

$71.6 \, \text{bpm} < \mu < 78.4 \, \text{bpm}$

This interval suggests that we are 90% confident the true mean pulse rate for adult females falls within this range.

Here’s a summary of the calculations:

• Sample mean ($\bar{x}$) = 75.0 bpm
• Sample standard deviation ($s$) = 13.2 bpm (rounded to one decimal place)

Would you like further details on how these values were calculated or comparisons with male pulse rates?

Additional Questions

1. How do we determine the sample size requirement for different confidence levels?
2. What effect does increasing the confidence level have on the interval width?
3. How would using a t-score instead of a z-score affect this interval, especially with smaller samples?
4. How does this confidence interval compare with that for adult males?
5. How can we interpret this confidence interval in practical terms?

Tip:

Remember that increasing sample size decreases the margin of error, leading to a narrower confidence interval for the same confidence level.