M... CF Ha: μs 1219.47 OE. Ho: μs 1219.47 Ha: μ> 1219.47 U Ha: μ> 1190 OF. Ho: μ> 1190 Ha: μ≤ 1190 Calculate the standardized test statistic. The standardized test statistic is 2.50, (Round to two decimal places as needed.) Determine the P-value.
M... CF Ha: μs 1219.47 OE. Ho: μs 1219.47 Ha: μ> 1219.47 U Ha: μ> 1190 OF. Ho: μ> 1190 Ha: μ≤ 1190 Calculate the standardized test statistic. The standardized test statistic is 2.50, (Round to two decimal places as needed.) Determine the P-value.
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 Population Mean**
In this section, we will learn how to test a claim about the population mean, \(\mu\), at a specified level of significance, \(\alpha\), using the given sample statistics. We assume the population is normally distributed.
**Example Problem:**
**Claim:** \(\mu \leq 1190\); \(\alpha = 0.09\); \(\sigma = 204.44\). Sample statistics: \(\overline{x} = 1219.47\), \(n = 300\).
### Possible Hypotheses:
You need to choose the appropriate hypothesis to test the given claim. The hypotheses options are:
- **Option A:**
\[
\begin{align*}
H_0: \mu > 1219.47 \\
H_a: \mu \leq 1219.47
\end{align*}
\]
- **Option B:**
\[
\begin{align*}
H_0: \mu < 1219.47 \\
H_a: \mu \geq 1219.47
\end{align*}
\]
- **Option C:**
\[
\begin{align*}
H_0: \mu = 1219.47 \\
H_a: \mu \neq 1219.47
\end{align*}
\]
- **Option D:**
\[
\begin{align*}
H_0: \mu = 1190 \\
H_a: \mu \neq 1190
\end{align*}
\]
- **Option E:**
\[
\begin{align*}
H_0: \mu \leq 1219.47 \\
H_a: \mu > 1219.47
\end{align*}
\]
- **Option F:**
\[
\begin{align*}
H_0: \mu > 1190 \\
H_a: \mu \leq 1190
\end{align*}
\]
### Calculate the Standardized Test Statistic:
Next, we calculate the standardized test statistic using the formula:
\[
z = \frac{\overline{x}](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F952bcd3e-4a7c-474a-8dd6-ddd08471460a%2Fe0b3c31b-5ea4-4f9e-b0f4-43eba2740499%2Fq0razy_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Hypothesis Testing for Population Mean**
In this section, we will learn how to test a claim about the population mean, \(\mu\), at a specified level of significance, \(\alpha\), using the given sample statistics. We assume the population is normally distributed.
**Example Problem:**
**Claim:** \(\mu \leq 1190\); \(\alpha = 0.09\); \(\sigma = 204.44\). Sample statistics: \(\overline{x} = 1219.47\), \(n = 300\).
### Possible Hypotheses:
You need to choose the appropriate hypothesis to test the given claim. The hypotheses options are:
- **Option A:**
\[
\begin{align*}
H_0: \mu > 1219.47 \\
H_a: \mu \leq 1219.47
\end{align*}
\]
- **Option B:**
\[
\begin{align*}
H_0: \mu < 1219.47 \\
H_a: \mu \geq 1219.47
\end{align*}
\]
- **Option C:**
\[
\begin{align*}
H_0: \mu = 1219.47 \\
H_a: \mu \neq 1219.47
\end{align*}
\]
- **Option D:**
\[
\begin{align*}
H_0: \mu = 1190 \\
H_a: \mu \neq 1190
\end{align*}
\]
- **Option E:**
\[
\begin{align*}
H_0: \mu \leq 1219.47 \\
H_a: \mu > 1219.47
\end{align*}
\]
- **Option F:**
\[
\begin{align*}
H_0: \mu > 1190 \\
H_a: \mu \leq 1190
\end{align*}
\]
### Calculate the Standardized Test Statistic:
Next, we calculate the standardized test statistic using the formula:
\[
z = \frac{\overline{x}
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