Ho: 18.7 meters, Ha: 18.7 meters, n = 49, x= 19.5 meters, a = 1.4 meters the value of the standard score is Round to two decimal places as needed.) the critical value(s) is/are Use a comma to separate answers as needed. Round to two decimal places as needed.) Determine whether the alternative hypothesis is supported at a 0.05 significance level. OA. The standard score is at least as extreme as the critical value(s). Reject Ho. The alternative hypothesis is supported. OB. The standard score is at least as extreme as the critical value(s). Do not reject Ho. The alternative hypothesis is not supported. OC. The standard score is less extreme than the critical value(s). Reject Ho. The alternative hypothesis is supported. OD. The standard score is less extreme than the critical value(s). Do not reject Ho. The alternative hypothesis is not supported.
Ho: 18.7 meters, Ha: 18.7 meters, n = 49, x= 19.5 meters, a = 1.4 meters the value of the standard score is Round to two decimal places as needed.) the critical value(s) is/are Use a comma to separate answers as needed. Round to two decimal places as needed.) Determine whether the alternative hypothesis is supported at a 0.05 significance level. OA. The standard score is at least as extreme as the critical value(s). Reject Ho. The alternative hypothesis is supported. OB. The standard score is at least as extreme as the critical value(s). Do not reject Ho. The alternative hypothesis is not supported. OC. The standard score is less extreme than the critical value(s). Reject Ho. The alternative hypothesis is supported. OD. The standard score is less extreme than the critical value(s). Do not reject Ho. The alternative hypothesis is not supported.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
![### Hypothesis Testing: Evaluating the Standard Score
This section guides you through the process of finding the value of the standard score \( z \) and determining whether to reject the null hypothesis at a 0.05 significance level. The question asks if the alternative hypothesis is supported based on the provided data.
---
**Given Data:**
- Null Hypothesis (\( H_0 \)): \( \mu = 18.7 \) meters
- Alternative Hypothesis (\( H_a \)): \( \mu \neq 18.7 \) meters
- Sample Size (\( n \)): 49
- Sample Mean (\(\bar{x}\)): 19.5 meters
- Population Standard Deviation (\( \sigma \)): 1.4 meters
---
**Task Instructions:**
1. **Calculate the Standard Score (\( z \)):**
\[
\text{The value of the standard score is:} \hspace{10pt} \_\_\_\_.
\]
*(Round to two decimal places as needed.)*
2. **Determine the Critical Values:**
\[
\text{The critical value(s) is/are:} \hspace{10pt} \_\_\_\_.
\]
*(Use a comma to separate answers as needed. Round to two decimal places as needed.)*
---
**Final Step: Determine whether the alternative hypothesis is supported at a 0.05 significance level.**
**Choices:**
- **A.** The standard score is at least as extreme as the critical value(s). Reject \( H_0 \). The alternative hypothesis is supported.
- **B.** The standard score is at least as extreme as the critical value(s). Do not reject \( H_0 \). The alternative hypothesis is not supported.
- **C.** The standard score is less extreme than the critical value(s). Reject \( H_0 \). The alternative hypothesis is supported.
- **D.** The standard score is less extreme than the critical value(s). Do not reject \( H_0 \). The alternative hypothesis is not supported.
---
**Explanation:**
To solve the problem accurately:
1. Calculate the \( z \)-score using the formula for the standard score:
\[
z = \frac{\bar{x} - \mu}{\sigma / \sqrt{n}}
\]
2. Find the critical values from the](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1a448b68-b882-4133-a49b-44585a3f695e%2F3478c897-fb5b-43c4-8efe-1b8b85a67586%2F990lkdd_processed.png&w=3840&q=75)
Transcribed Image Text:### Hypothesis Testing: Evaluating the Standard Score
This section guides you through the process of finding the value of the standard score \( z \) and determining whether to reject the null hypothesis at a 0.05 significance level. The question asks if the alternative hypothesis is supported based on the provided data.
---
**Given Data:**
- Null Hypothesis (\( H_0 \)): \( \mu = 18.7 \) meters
- Alternative Hypothesis (\( H_a \)): \( \mu \neq 18.7 \) meters
- Sample Size (\( n \)): 49
- Sample Mean (\(\bar{x}\)): 19.5 meters
- Population Standard Deviation (\( \sigma \)): 1.4 meters
---
**Task Instructions:**
1. **Calculate the Standard Score (\( z \)):**
\[
\text{The value of the standard score is:} \hspace{10pt} \_\_\_\_.
\]
*(Round to two decimal places as needed.)*
2. **Determine the Critical Values:**
\[
\text{The critical value(s) is/are:} \hspace{10pt} \_\_\_\_.
\]
*(Use a comma to separate answers as needed. Round to two decimal places as needed.)*
---
**Final Step: Determine whether the alternative hypothesis is supported at a 0.05 significance level.**
**Choices:**
- **A.** The standard score is at least as extreme as the critical value(s). Reject \( H_0 \). The alternative hypothesis is supported.
- **B.** The standard score is at least as extreme as the critical value(s). Do not reject \( H_0 \). The alternative hypothesis is not supported.
- **C.** The standard score is less extreme than the critical value(s). Reject \( H_0 \). The alternative hypothesis is supported.
- **D.** The standard score is less extreme than the critical value(s). Do not reject \( H_0 \). The alternative hypothesis is not supported.
---
**Explanation:**
To solve the problem accurately:
1. Calculate the \( z \)-score using the formula for the standard score:
\[
z = \frac{\bar{x} - \mu}{\sigma / \sqrt{n}}
\]
2. Find the critical values from the
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