Construct the Indicated Confidence Interval for the Difference Between the Two

question 64

Multiple Choice

Construct the indicated confidence interval for the difference between the two population means. Assume that the two samples are independent simple random samples selected from normally distributed populations. Also assume that the population standard deviations are equal $\left( \sigma _ { 1 } = \sigma _ { 2 } \right)$ , so that the standard error of the difference between means is obtained by pooling the sample variances .
-A researcher was interested in comparing the resting pulse rates of people who exercise regularly and people who do not exercise regularly. Independent simple random samples were obtained of 16 people who do not exercise regularly and 12 people who do exercise regularly. The resting pulse
Rate (in beats per minute) of each person was recorded. The summary statistics are as follows. $\begin{array}{r|r}\text { Do Not Exercise } & \text { Do Exercise } \\\hline \overline{\mathrm{x}}_{1}=73.4 \text { beats } / \mathrm{min} & \overline{\mathrm{x}}_{2}=68.7 \text { beats } / \mathrm{min} \\\mathrm{s}_{1}=10.1 \text { beats } / \mathrm{min} & \mathrm{s}_{2}=8.4 \text { beat } / \mathrm{min} \\\mathrm{n}_{1}=16 & \mathrm{n}_{2}=12\end{array}$
Construct a $90 \%$ confidence interval for the difference between the mean pulse rate of people who do not exercise regularly and the mean pulse rate of people who exercise regularly.

• A) \(- 1.44\) beats \(/ \mathrm { min } < \mu _ { 1 } - \mu _ { 2 } < 10.84\) beats \(/ \mathrm { min }\)
• B) \(- 0.03\) beats \(/ \mathrm { min } < \mu _ { 1 } - \mu _ { 2 } < 9.43\) beats \(/ \mathrm { min }\)
• C) \(0.74\) beats \(/ \mathrm { min } < \mu _ { 1 } - \mu _ { 2 } < 8.66\) beats \(/ \mathrm { min }\)
• D) \(- 2.08\) beats \(/ \mathrm { min } < \mu _ { 1 } - \mu _ { 2 } < 11.48\) beats \(/ \mathrm { min }\)

---

Definitions:

Testosterone

is a primary male sex hormone that plays key roles in health and well-being, including the development of male reproductive tissues and secondary sexual characteristics.

Estrogen

A group of hormones playing a crucial role in the development and regulation of the female reproductive system and secondary sex characteristics.

Y Chromosome

A sex chromosome that is typically present in males, combined with an X chromosome, and determines male biological characteristics in humans.

Testosterone

A steroid hormone associated with male sex characteristics, although present in both genders, affecting mood, energy, and physical development.