Test the claim about the population mean μ at the level of significance a. Assume the population is normally distributed. Claim: μ<4815; a=0.01 Sample statistics: x=4917, s=5501, n = 53 What are the null and alternative hypotheses? Ho: На ▼ (Type integers or decimals. Do not round.) Find the standardized test statistic t. ▼ ▼ t= (Round to two decimal places as needed.) Find the P-value. P= (Round to three decimal places as needed.) Decide whether to reject or fail to reject the null hypothesis. enough evidence at the Ho. There Choose the correct answer below. % level of significance to the claim.
Test the claim about the population mean μ at the level of significance a. Assume the population is normally distributed. Claim: μ<4815; a=0.01 Sample statistics: x=4917, s=5501, n = 53 What are the null and alternative hypotheses? Ho: На ▼ (Type integers or decimals. Do not round.) Find the standardized test statistic t. ▼ ▼ t= (Round to two decimal places as needed.) Find the P-value. P= (Round to three decimal places as needed.) Decide whether to reject or fail to reject the null hypothesis. enough evidence at the Ho. There Choose the correct answer below. % level of significance to the claim.
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 for the Population Mean
**Objective:** Test the claim about the population mean (\(\mu\)) at the level of significance (\(\alpha\)). Assume the population is normally distributed.
- **Given claim:** \(\mu < 4815\)
- **Level of significance:** \(\alpha = 0.01\)
- **Sample statistics:**
- Sample mean (\(\bar{x}\)) = 4917
- Sample standard deviation (\(s\)) = 5501
- Sample size (\(n\)) = 53
#### Steps to Perform the Hypothesis Test
1. **Set Up Hypotheses:**
- Null hypothesis (\(H_0\)): \(\mu \geq 4815\)
- Alternative hypothesis (\(H_a\)): \(\mu < 4815\)
(Type integers or decimals. Do not round.)
2. **Find the Standardized Test Statistic:** Calculate the test statistic \(t\) using the formula:
\[
t = \frac{\bar{x} - \mu_0}{\frac{s}{\sqrt{n}}}
\]
- Round to two decimal places as needed.
3. **Find the P-value:**
- Round to three decimal places as needed.
4. **Decision Rule:** Decide whether to reject or fail to reject the null hypothesis:
- Determine if there is enough evidence at the 1% level of significance to reject the null hypothesis.
- Formal statement: \(H_0\): There is \(\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\) enough evidence at the \(\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\) % level of significance to \(\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\) the claim.
#### Explanation of Graphs or Diagrams (If Any)
- There are no graphs or diagrams accompanying this problem statement.
This structured approach ensures clarity while presenting hypothesis testing in an educational context, aiding students in understanding the mechanics and interpretation of statistical tests effectively.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F15e40907-5866-4802-8bee-6781a38984f9%2F4e6ca7f5-b24f-4af2-a37d-378adace0265%2Fuh2sq_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Hypothesis Testing for the Population Mean
**Objective:** Test the claim about the population mean (\(\mu\)) at the level of significance (\(\alpha\)). Assume the population is normally distributed.
- **Given claim:** \(\mu < 4815\)
- **Level of significance:** \(\alpha = 0.01\)
- **Sample statistics:**
- Sample mean (\(\bar{x}\)) = 4917
- Sample standard deviation (\(s\)) = 5501
- Sample size (\(n\)) = 53
#### Steps to Perform the Hypothesis Test
1. **Set Up Hypotheses:**
- Null hypothesis (\(H_0\)): \(\mu \geq 4815\)
- Alternative hypothesis (\(H_a\)): \(\mu < 4815\)
(Type integers or decimals. Do not round.)
2. **Find the Standardized Test Statistic:** Calculate the test statistic \(t\) using the formula:
\[
t = \frac{\bar{x} - \mu_0}{\frac{s}{\sqrt{n}}}
\]
- Round to two decimal places as needed.
3. **Find the P-value:**
- Round to three decimal places as needed.
4. **Decision Rule:** Decide whether to reject or fail to reject the null hypothesis:
- Determine if there is enough evidence at the 1% level of significance to reject the null hypothesis.
- Formal statement: \(H_0\): There is \(\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\) enough evidence at the \(\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\) % level of significance to \(\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\) the claim.
#### Explanation of Graphs or Diagrams (If Any)
- There are no graphs or diagrams accompanying this problem statement.
This structured approach ensures clarity while presenting hypothesis testing in an educational context, aiding students in understanding the mechanics and interpretation of statistical tests effectively.
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