You wish to test the following claim (H) at a significance level of a = 0.10. H.:p = 0.11 H:p< 0.11 You obtain a sample of size n 169 in which there are 8 successful observations. Determine the test statistic formula for this test. What is the test statistic for this sample? (Report answer accurate to three decimal places.) test statistic What is the p-value for this sample? (Report answer accurate to four decimal places.) p-value = The p-value is... O less than (or equal to) a greater than a This test statistic leads to a decision to... O reject the null O accept the null
You wish to test the following claim (H) at a significance level of a = 0.10. H.:p = 0.11 H:p< 0.11 You obtain a sample of size n 169 in which there are 8 successful observations. Determine the test statistic formula for this test. What is the test statistic for this sample? (Report answer accurate to three decimal places.) test statistic What is the p-value for this sample? (Report answer accurate to four decimal places.) p-value = The p-value is... O less than (or equal to) a greater than a This test statistic leads to a decision to... O reject the null O accept the null
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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![# Hypothesis Testing Example
### Problem Statement
You wish to test the following claim (\( H_a \)) at a significance level of \( \alpha = 0.10 \):
- \( H_0 \): \( p = 0.11 \)
- \( H_a \): \( p < 0.11 \)
You obtain a sample of size \( n = 169 \) in which there are 8 successful observations.
### Steps for Hypothesis Testing
#### 1. Determine the test statistic formula for this test.
The test statistic for a proportion is usually given by:
\[
z = \frac{\hat{p} - p_0}{\sqrt{\frac{p_0(1 - p_0)}{n}}}
\]
where:
- \(\hat{p}\) is the sample proportion
- \(p_0\) is the hypothesized population proportion
- \(n\) is the sample size
#### 2. Calculate the test statistic for this sample.
(Report answer accurate to three decimal places.)
\[
\text{test statistic} = \_\_\_\_\_
\]
#### 3. Determine the p-value for this sample.
(Report answer accurate to four decimal places.)
\[
\text{p-value} = \_\_\_\_\_
\]
### Decision Making
The p-value is…
- \( \circ \) less than (or equal to) \( \alpha \)
- \( \circ \) greater than \( \alpha \)
This test statistic leads to a decision to…
- \( \circ \) reject the null
- \( \circ \) accept the null
- \( \circ \) fail to reject the null
### Conclusion
Based on the p-value, you'll make a decision to either reject the null hypothesis \( H_0 \) or fail to reject it, thereby supporting the alternative hypothesis \( H_a \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fae9dff02-6614-4387-a434-63ee01638e81%2Fb50da973-fe53-412b-8d8c-39dcd42084d8%2F96rgyq_processed.jpeg&w=3840&q=75)
Transcribed Image Text:# Hypothesis Testing Example
### Problem Statement
You wish to test the following claim (\( H_a \)) at a significance level of \( \alpha = 0.10 \):
- \( H_0 \): \( p = 0.11 \)
- \( H_a \): \( p < 0.11 \)
You obtain a sample of size \( n = 169 \) in which there are 8 successful observations.
### Steps for Hypothesis Testing
#### 1. Determine the test statistic formula for this test.
The test statistic for a proportion is usually given by:
\[
z = \frac{\hat{p} - p_0}{\sqrt{\frac{p_0(1 - p_0)}{n}}}
\]
where:
- \(\hat{p}\) is the sample proportion
- \(p_0\) is the hypothesized population proportion
- \(n\) is the sample size
#### 2. Calculate the test statistic for this sample.
(Report answer accurate to three decimal places.)
\[
\text{test statistic} = \_\_\_\_\_
\]
#### 3. Determine the p-value for this sample.
(Report answer accurate to four decimal places.)
\[
\text{p-value} = \_\_\_\_\_
\]
### Decision Making
The p-value is…
- \( \circ \) less than (or equal to) \( \alpha \)
- \( \circ \) greater than \( \alpha \)
This test statistic leads to a decision to…
- \( \circ \) reject the null
- \( \circ \) accept the null
- \( \circ \) fail to reject the null
### Conclusion
Based on the p-value, you'll make a decision to either reject the null hypothesis \( H_0 \) or fail to reject it, thereby supporting the alternative hypothesis \( H_a \).
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