We appreciate your visit to Checking the Large Counts Condition for a Two Proportion tex z tex Test A researcher wants to know if people who exercise with others are. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!
Answer :
- Calculate the number of people still exercising in each group: $x_1 = 100 \cdot 0.58 = 58$ and $x_2 = 100 \cdot 0.18 = 18$.
- Calculate the pooled proportion: $\hat{p} = \frac{58 + 18}{100 + 100} = 0.38$.
- Identify the given values: $\hat{p}_c = 0.58$, $\hat{p}_A = 0.18$, $n_1 = 100$, $n_2 = 100$.
- The final pooled proportion is: $\boxed{0.38}$.
### Explanation
1. Understand the problem and provided data
We are given the following information:
* The proportion of adults who exercised with others and were still exercising after one year is $\hat{p}_c = 0.58$.
* The proportion of adults who exercised alone and were still exercising after one year is $\hat{p}_A = 0.18$.
* The number of adults who exercised with others is $n_1 = 100$.
* The number of adults who exercised alone is $n_2 = 100$.
We need to find the values for $\hat{p}_c$, $\hat{p}_A$, $n_1$, $n_2$, and $\hat{p}$, where $\hat{p} = \frac{x_1 + x_2}{n_1 + n_2}$, $x_1$ is the number of people in the first group who were still exercising and $x_2$ is the number of people in the second group who were still exercising.
2. Calculate the number of people still exercising in each group
First, we need to find the number of people in each group who were still exercising after one year.
For the group that exercised with others:
$$x_1 = n_1 \cdot \hat{p}_c = 100 \cdot 0.58 = 58$$
For the group that exercised alone:
$$x_2 = n_2 \cdot \hat{p}_A = 100 \cdot 0.18 = 18$$
3. Calculate the pooled proportion
Now, we can calculate the pooled proportion $\hat{p}$:
$$\hat{p} = \frac{x_1 + x_2}{n_1 + n_2} = \frac{58 + 18}{100 + 100} = \frac{76}{200} = 0.38$$
4. State the final answer
So, we have:
* $\hat{p}_c = 0.58$
* $\hat{p}_A = 0.18$
* $n_1 = 100$
* $n_2 = 100$
* $\hat{p} = 0.38$
Therefore, the values are:
$\hat{p}_c=58 \text{ out of } 100=0.58$
$\hat{p}_A=18 \text{ out of } 100=0.18$
$\begin{array}{l}
n_1=100 \\
n_2=100\quad
\end{array}$
$\hat{p}=\frac{x_1+x_2}{n_1+n_2}=0.38$
### Examples
This type of two-proportion z-test is often used in medical research to compare the effectiveness of two different treatments. For example, a researcher might want to compare the success rates of a new drug versus a placebo in treating a particular condition. By calculating the proportions of patients who respond positively to each treatment, they can determine whether the new drug is significantly more effective than the placebo. This helps in making informed decisions about which treatments to use in clinical practice.
- Calculate the pooled proportion: $\hat{p} = \frac{58 + 18}{100 + 100} = 0.38$.
- Identify the given values: $\hat{p}_c = 0.58$, $\hat{p}_A = 0.18$, $n_1 = 100$, $n_2 = 100$.
- The final pooled proportion is: $\boxed{0.38}$.
### Explanation
1. Understand the problem and provided data
We are given the following information:
* The proportion of adults who exercised with others and were still exercising after one year is $\hat{p}_c = 0.58$.
* The proportion of adults who exercised alone and were still exercising after one year is $\hat{p}_A = 0.18$.
* The number of adults who exercised with others is $n_1 = 100$.
* The number of adults who exercised alone is $n_2 = 100$.
We need to find the values for $\hat{p}_c$, $\hat{p}_A$, $n_1$, $n_2$, and $\hat{p}$, where $\hat{p} = \frac{x_1 + x_2}{n_1 + n_2}$, $x_1$ is the number of people in the first group who were still exercising and $x_2$ is the number of people in the second group who were still exercising.
2. Calculate the number of people still exercising in each group
First, we need to find the number of people in each group who were still exercising after one year.
For the group that exercised with others:
$$x_1 = n_1 \cdot \hat{p}_c = 100 \cdot 0.58 = 58$$
For the group that exercised alone:
$$x_2 = n_2 \cdot \hat{p}_A = 100 \cdot 0.18 = 18$$
3. Calculate the pooled proportion
Now, we can calculate the pooled proportion $\hat{p}$:
$$\hat{p} = \frac{x_1 + x_2}{n_1 + n_2} = \frac{58 + 18}{100 + 100} = \frac{76}{200} = 0.38$$
4. State the final answer
So, we have:
* $\hat{p}_c = 0.58$
* $\hat{p}_A = 0.18$
* $n_1 = 100$
* $n_2 = 100$
* $\hat{p} = 0.38$
Therefore, the values are:
$\hat{p}_c=58 \text{ out of } 100=0.58$
$\hat{p}_A=18 \text{ out of } 100=0.18$
$\begin{array}{l}
n_1=100 \\
n_2=100\quad
\end{array}$
$\hat{p}=\frac{x_1+x_2}{n_1+n_2}=0.38$
### Examples
This type of two-proportion z-test is often used in medical research to compare the effectiveness of two different treatments. For example, a researcher might want to compare the success rates of a new drug versus a placebo in treating a particular condition. By calculating the proportions of patients who respond positively to each treatment, they can determine whether the new drug is significantly more effective than the placebo. This helps in making informed decisions about which treatments to use in clinical practice.
Thanks for taking the time to read Checking the Large Counts Condition for a Two Proportion tex z tex Test A researcher wants to know if people who exercise with others are. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!
- Why do Businesses Exist Why does Starbucks Exist What Service does Starbucks Provide Really what is their product.
- The pattern of numbers below is an arithmetic sequence tex 14 24 34 44 54 ldots tex Which statement describes the recursive function used to..
- Morgan felt the need to streamline Edison Electric What changes did Morgan make.
Rewritten by : Barada
