22.6 is what needs answerd the other is just what goes with it please use calculator method use a ti83 or 84 to answer please **Example 22.4: Estimating Risky Behavior****State:** The National AIDS Behavioral Survey found that 170 of a sample of 2673 adult heterosexuals had multiple partners. That is, \[\hat{p} = \frac{170}{2673} = 0.0636\]What can we say about the population of all adult heterosexuals?**Plan:** We will give a 99% confidence interval to estimate the proportion, $ p $, of all adult heterosexuals who have multiple partners.**Solution:** First, verify the conditions for inference:1. Sample must be a simple random sample (SRS). The sampling design for this survey was complex and stratified, but it is approximately close to an SRS.2. The sampling distribution of $\hat{p}$ must be approximately Normal. We check if $np$ and $n(1-p)$ are both greater than 10.3. The sample size condition is easily satisfied since n = 2673, which is large.Next, calculate the confidence interval for the proportion $ p $. A 99% confidence interval uses the standard Normal critical value $ z^* = 2.576 $. The confidence interval is given by:\[\hat{p} \pm z^* \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}\]Substitute the values:\[0.0636 \pm 2.576 \sqrt{\frac{(0.0636)(0.9364)}{2673}}\]Calculate:\[0.0636 \pm 0.0122 = [0.0514, 0.0758]\]**Conclude:** We are 99% confident that the percent of adult heterosexuals who have had more than one sexual partner in the past year is between about 5.1% and 7.6%.**Note:** This example outlines the statistical process of estimating a population proportion and illustrates constructing a confidence interval for practical applications in public health research. **Weightlifting Injuries**Resistance training is a popular form of conditioning aimed at enhancing sports performance and is widely used among high school, college, and professional athletes, although its use for younger athletes is controversial. A random sample of 4,111 patients aged 8-30 admitted to U.S. emergency rooms with the Consumer Product Safety Commission code "weightlifting" were obtained. These injuries were classified as "accidental" if caused by dropped weight or improper equipment use. Of the 4,111 weightlifting injuries, 1,552 were classified as accidental. Give a 90% confidence interval for the proportion of weightlifting injuries in this age group that were accidental. Follow the four-step process as illustrated in Example 22.4.

Given: Sample size, n = 4111 Number of injuries classified as accidental = 1552 The sample proportion of injuries classified as accidental, p^ =1552/4111 =0.38 The condition that the sample is randomly selected is satisfied as it is already stated in the problem. Since the sample is large, we see that np^ = 4111×0.38 = 1562.18 >15, the sampling distribution of the sample proportion is approximately normal. A 90% confidence interval for the population proportion, p, of injuries classified as accidental is given by p^ ± zα/2×p^(1-p^)/n= 0.38 ± 1.645×0.38×0.62/4111= 0.38 ± 0.012= 0.386 to 0.392 Conclusion: We are 90% confident that the population proportion of injuries classified as accidental lies between 0.386 and 0.392.

Math

Statistics

Weightlifting Injuries. Resistance training is a popular form of condition enhancing sports performance and is widely used among high ing aimed at school, college, and professional athletes, although its use for is controversial. A random sample of 4111 patients aged 8-30 admitted to younger athletes U.S. emergency rooms with the Consumer Product Safety Commission code "weightlifting" were obtained. These injuries were classified as "accidental" if caused by dropped weight or improper equipment use. Of the 4111 weight- lifting injuries, 1552 were classified as accidental.0 Give a 90% confidence interval for the proportion of weightlifting injuries in this age group that were accidental. Follow the four-step process as illustrated in Example 22.4.

Weightlifting Injuries. Resistance training is a popular form of condition enhancing sports performance and is widely used among high ing aimed at school, college, and professional athletes, although its use for is controversial. A random sample of 4111 patients aged 8-30 admitted to younger athletes U.S. emergency rooms with the Consumer Product Safety Commission code "weightlifting" were obtained. These injuries were classified as "accidental" if caused by dropped weight or improper equipment use. Of the 4111 weight- lifting injuries, 1552 were classified as accidental.0 Give a 90% confidence interval for the proportion of weightlifting injuries in this age group that were accidental. Follow the four-step process as illustrated in Example 22.4.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

22.6 is what needs answerd the other is just what goes with it please use calculator method use a ti83 or 84 to answer please

**Example 22.4: Estimating Risky Behavior**

**State:**
The National AIDS Behavioral Survey found that 170 of a sample of 2673 adult heterosexuals had multiple partners. That is,

\[
\hat{p} = \frac{170}{2673} = 0.0636
\]

What can we say about the population of all adult heterosexuals?

**Plan:**
We will give a 99% confidence interval to estimate the proportion, $ p $, of all adult heterosexuals who have multiple partners.

**Solution:**
First, verify the conditions for inference:

1. Sample must be a simple random sample (SRS). The sampling design for this survey was complex and stratified, but it is approximately close to an SRS.
2. The sampling distribution of $\hat{p}$ must be approximately Normal. We check if $np$ and $n(1-p)$ are both greater than 10.
3. The sample size condition is easily satisfied since n = 2673, which is large.

Next, calculate the confidence interval for the proportion $ p $. A 99% confidence interval uses the standard Normal critical value $ z^* = 2.576 $. The confidence interval is given by:

\[
\hat{p} \pm z^* \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}
\]

Substitute the values:

\[
0.0636 \pm 2.576 \sqrt{\frac{(0.0636)(0.9364)}{2673}}
\]

Calculate:

\[
0.0636 \pm 0.0122 = [0.0514, 0.0758]
\]

**Conclude:**
We are 99% confident that the percent of adult heterosexuals who have had more than one sexual partner in the past year is between about 5.1% and 7.6%.

**Note:**
This example outlines the statistical process of estimating a population proportion and illustrates constructing a confidence interval for practical applications in public health research.

**Weightlifting Injuries**

Resistance training is a popular form of conditioning aimed at enhancing sports performance and is widely used among high school, college, and professional athletes, although its use for younger athletes is controversial. A random sample of 4,111 patients aged 8-30 admitted to U.S. emergency rooms with the Consumer Product Safety Commission code "weightlifting" were obtained. These injuries were classified as "accidental" if caused by dropped weight or improper equipment use. Of the 4,111 weightlifting injuries, 1,552 were classified as accidental.

Give a 90% confidence interval for the proportion of weightlifting injuries in this age group that were accidental. Follow the four-step process as illustrated in Example 22.4.

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