(a) Use a calculator with mean and standard deviation keys to calculate x,, s,, X2, and s3. (Round your answers to four decimal places.) X2 =| $2 (b) Let u, be the population mean for x, and let u, be the population mean for x3. Find 99% confidence interval for Hy - H2. (Round your answers to one decimal place.) lower limit upper limit (c) Examine the confidence interval and explain what it means in the context of this problem. Does the interval consist of numbers that are all positive? all negative? of different signs? At the 99% level of confidence, do professional football players tend to have a higher population mean weight than professional basketball players? O Because the interval contains only negative numbers, we can say that professional football players have a lower mean weight than professional basketball players. O Because the interval contains both positive and negative numbers, we cannot say that professional football players have a higher mean weight than professional basketball players. O Because the interval contains only positive numbers, we can say that professional football players have a higher mean weight than professional basketball players. (d) Which distribution did you use? Why? O The Student's t-distribution was used because o, and o, are unknown.
(a) Use a calculator with mean and standard deviation keys to calculate x,, s,, X2, and s3. (Round your answers to four decimal places.) X2 =| $2 (b) Let u, be the population mean for x, and let u, be the population mean for x3. Find 99% confidence interval for Hy - H2. (Round your answers to one decimal place.) lower limit upper limit (c) Examine the confidence interval and explain what it means in the context of this problem. Does the interval consist of numbers that are all positive? all negative? of different signs? At the 99% level of confidence, do professional football players tend to have a higher population mean weight than professional basketball players? O Because the interval contains only negative numbers, we can say that professional football players have a lower mean weight than professional basketball players. O Because the interval contains both positive and negative numbers, we cannot say that professional football players have a higher mean weight than professional basketball players. O Because the interval contains only positive numbers, we can say that professional football players have a higher mean weight than professional basketball players. (d) Which distribution did you use? Why? O The Student's t-distribution was used because o, and o, are unknown.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
![**Title: Comparing Weights of Professional Football and Basketball Players**
**Introduction:**
Independent random samples of professional football and basketball players provided the following weight data. The weight distributions are assumed to be mound-shaped and symmetric.
**Data:**
- **Weights (in lb) of pro football players**: \( x_1; \, n_1 = 21 \)
- 243, 262, 256, 251, 244, 276, 240, 265, 257, 252, 282, 256, 250, 264, 270, 275, 245, 275, 253, 265, 270
- **Weights (in lb) of pro basketball players**: \( x_2; \, n_2 = 19 \)
- 204, 200, 220, 210, 193, 215, 222, 216, 228, 207, 225, 208, 195, 191, 207, 196, 182, 193, 201
**Tasks:**
**(a) Calculating Means and Standard Deviations:**
Use a calculator to find the mean (\(\bar{x}_1\), \(\bar{x}_2\)) and standard deviation (\(s_1\), \(s_2\)) for the data sets. Round your answers to four decimal places.
\[
\begin{align*}
\bar{x}_1 &= \text{______} \\
s_1 &= \text{______} \\
\bar{x}_2 &= \text{______} \\
s_2 &= \text{______} \\
\end{align*}
\]
**(b) Confidence Interval Calculation:**
Let \(\mu_1\) be the population mean for \(x_1\) and \(\mu_2\) for \(x_2\). Find a 99% confidence interval for \(\mu_1 - \mu_2\). Round your answers to one decimal place.
\[
\begin{align*}
\text{lower limit} &= \text{______} \\
\text{upper limit} &= \text{______} \\
\end{align*}
\]
**(c) Analyzing the Confidence Interval:**
Examine the confidence interval and explain its meaning. Does it](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0a8d585f-99dd-4e5d-b593-c7eaddfe8ce4%2F29e98d36-cba2-4461-be68-ff1023a68ddd%2Fypelvi_processed.png&w=3840&q=75)
Transcribed Image Text:**Title: Comparing Weights of Professional Football and Basketball Players**
**Introduction:**
Independent random samples of professional football and basketball players provided the following weight data. The weight distributions are assumed to be mound-shaped and symmetric.
**Data:**
- **Weights (in lb) of pro football players**: \( x_1; \, n_1 = 21 \)
- 243, 262, 256, 251, 244, 276, 240, 265, 257, 252, 282, 256, 250, 264, 270, 275, 245, 275, 253, 265, 270
- **Weights (in lb) of pro basketball players**: \( x_2; \, n_2 = 19 \)
- 204, 200, 220, 210, 193, 215, 222, 216, 228, 207, 225, 208, 195, 191, 207, 196, 182, 193, 201
**Tasks:**
**(a) Calculating Means and Standard Deviations:**
Use a calculator to find the mean (\(\bar{x}_1\), \(\bar{x}_2\)) and standard deviation (\(s_1\), \(s_2\)) for the data sets. Round your answers to four decimal places.
\[
\begin{align*}
\bar{x}_1 &= \text{______} \\
s_1 &= \text{______} \\
\bar{x}_2 &= \text{______} \\
s_2 &= \text{______} \\
\end{align*}
\]
**(b) Confidence Interval Calculation:**
Let \(\mu_1\) be the population mean for \(x_1\) and \(\mu_2\) for \(x_2\). Find a 99% confidence interval for \(\mu_1 - \mu_2\). Round your answers to one decimal place.
\[
\begin{align*}
\text{lower limit} &= \text{______} \\
\text{upper limit} &= \text{______} \\
\end{align*}
\]
**(c) Analyzing the Confidence Interval:**
Examine the confidence interval and explain its meaning. Does it
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