A report by the Gallup Poll stated that on average a woman visits her physician 5.8 times a year. A researcher randomly selects 20 women and obtained onto the data below.
A report by the Gallup Poll stated that on average a woman visits her physician 5.8 times a year. A researcher randomly selects 20 women and obtained onto the data below.
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
Related questions
Question
A report by the Gallup Poll stated that on average a woman visits her physician 5.8 times a year. A researcher randomly selects 20 women and obtained onto the data below.
![**Text Transcription and Explanation for Educational Website:**
---
**Hypothesis Testing in Practice**
A report by Gallup Poll stated that, on average, a woman visits her physician 5.8 times a year. A researcher randomly selects 20 women and obtains the following data:
| 3 | 2 | 1 | 3 | 7 | 9 | 4 | 6 | 6 |
|---|---|---|---|---|---|---|---|---|
| 8 | 0 | 5 | 6 | 4 | 2 | 1 | 3 | 4 | 1 |
**Research Question:**
At \(\alpha = 0.05\), can it be concluded that the average is still 5.8 visits per year?
**a) Identifying Hypothesis Test Requirements:**
Based on the problem description, how do we know that we are working with hypotheses \(H_0\) (null hypothesis) and \(H_1\) (alternative hypothesis)? This question has two possible answers:
- [ ] Asks us to find (estimate) the % confidence interval of the population (true) mean.
- [ ] Asks us to find (estimate) the % confidence interval of the population (true) proportion.
- [x] \(\alpha\) is provided.
- [x] Asks if there is evidence or can we conclude something.
- [ ] Asks us to find the sample size (how many or how large).
**Formulation of Hypotheses:**
- **Null Hypothesis (\(H_0\))**: \( \mu = 5.8 \)
- Claim: The average number of visits is 5.8.
- **Alternative Hypothesis (\(H_1\))**: \( \mu \neq 5.8 \)
- Not the claim: The average number of visits is different from 5.8.
**b) Selecting the Correct Normal Distribution:**
Please select the correct normal distribution based on our \(H_1\).
---
This section allows students to explore hypothesis testing by comparing sample data to a known population mean. The activity includes hypothesis formulation and selection of appropriate test criteria, using the provided significance level \(\alpha\).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Faa466c24-bbae-451a-a078-10dcd226e22a%2F78fe4019-c73a-403c-bc4e-5137b11317e6%2Fq7f6il_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Text Transcription and Explanation for Educational Website:**
---
**Hypothesis Testing in Practice**
A report by Gallup Poll stated that, on average, a woman visits her physician 5.8 times a year. A researcher randomly selects 20 women and obtains the following data:
| 3 | 2 | 1 | 3 | 7 | 9 | 4 | 6 | 6 |
|---|---|---|---|---|---|---|---|---|
| 8 | 0 | 5 | 6 | 4 | 2 | 1 | 3 | 4 | 1 |
**Research Question:**
At \(\alpha = 0.05\), can it be concluded that the average is still 5.8 visits per year?
**a) Identifying Hypothesis Test Requirements:**
Based on the problem description, how do we know that we are working with hypotheses \(H_0\) (null hypothesis) and \(H_1\) (alternative hypothesis)? This question has two possible answers:
- [ ] Asks us to find (estimate) the % confidence interval of the population (true) mean.
- [ ] Asks us to find (estimate) the % confidence interval of the population (true) proportion.
- [x] \(\alpha\) is provided.
- [x] Asks if there is evidence or can we conclude something.
- [ ] Asks us to find the sample size (how many or how large).
**Formulation of Hypotheses:**
- **Null Hypothesis (\(H_0\))**: \( \mu = 5.8 \)
- Claim: The average number of visits is 5.8.
- **Alternative Hypothesis (\(H_1\))**: \( \mu \neq 5.8 \)
- Not the claim: The average number of visits is different from 5.8.
**b) Selecting the Correct Normal Distribution:**
Please select the correct normal distribution based on our \(H_1\).
---
This section allows students to explore hypothesis testing by comparing sample data to a known population mean. The activity includes hypothesis formulation and selection of appropriate test criteria, using the provided significance level \(\alpha\).
![### Educational Text
**c) To find our Critical Value(s) (CV), will we use invNorm(), invT()?**
- Selected option: `invT()`
**d) Please explain the reason for the correct answer for step c.**
- Selected reason: `The population standard deviation is not given`
**Critical Values:**
- \( \text{CV}_1 = \text{invT}() \)
- Enter an integer or decimal number.
- \( \text{CV}_2 = \text{invT}() \)
- Enter an integer or decimal number.
**Round to Two Decimal Places:**
- \( \text{CV}_1 = \) [____]
- \( \text{CV}_2 = \) [____]
**f) What formula will we use for the test value?**
The formula for the test value is:
\[
O_z = \frac{(\hat{p}_1 - \hat{p}_2) - (p_1 - p_2)}{\sqrt{\hat{p} \cdot \hat{q} \cdot \left( \frac{1}{n_1} + \frac{1}{n_2} \right) }}
\]
This setup is for performing hypothesis tests where the population standard deviation is not given, thus requiring the use of the t-distribution for critical values. The formula provided is used to calculate the z test statistic for comparing two proportions.
Note: The page reflects an interactive input area to enter calculated values for critical values and test statistics rounded to two decimal places.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Faa466c24-bbae-451a-a078-10dcd226e22a%2F78fe4019-c73a-403c-bc4e-5137b11317e6%2F7wnv598_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Educational Text
**c) To find our Critical Value(s) (CV), will we use invNorm(), invT()?**
- Selected option: `invT()`
**d) Please explain the reason for the correct answer for step c.**
- Selected reason: `The population standard deviation is not given`
**Critical Values:**
- \( \text{CV}_1 = \text{invT}() \)
- Enter an integer or decimal number.
- \( \text{CV}_2 = \text{invT}() \)
- Enter an integer or decimal number.
**Round to Two Decimal Places:**
- \( \text{CV}_1 = \) [____]
- \( \text{CV}_2 = \) [____]
**f) What formula will we use for the test value?**
The formula for the test value is:
\[
O_z = \frac{(\hat{p}_1 - \hat{p}_2) - (p_1 - p_2)}{\sqrt{\hat{p} \cdot \hat{q} \cdot \left( \frac{1}{n_1} + \frac{1}{n_2} \right) }}
\]
This setup is for performing hypothesis tests where the population standard deviation is not given, thus requiring the use of the t-distribution for critical values. The formula provided is used to calculate the z test statistic for comparing two proportions.
Note: The page reflects an interactive input area to enter calculated values for critical values and test statistics rounded to two decimal places.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 2 images
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, probability and related others by exploring similar questions and additional content below.Recommended textbooks for you
A First Course in Probability (10th Edition)
Probability
ISBN:
9780134753119
Author:
Sheldon Ross
Publisher:
PEARSON
A First Course in Probability (10th Edition)
Probability
ISBN:
9780134753119
Author:
Sheldon Ross
Publisher:
PEARSON