**Hypothesis Testing: Population Mean****Context:**Use technology to help you test the claim about the population mean, $ \mu $, at the given level of significance, $ \alpha $, using the given sample statistics. Assume the population is normally distributed.**Claim:**\[ \mu \geq 1280 \]- Significance level, $ \alpha = 0.07 $- Population standard deviation, $ \sigma = 196.31 $- Sample statistics: $ \bar{x} = 1308.11 $, $ n = 200 $**Hypotheses Options:****Option A:** (Selected)- Null Hypothesis ($ H_0 $): $ \mu \leq 1280 $- Alternative Hypothesis ($ H_a $): $ \mu > 1280 $**Option B:**- Null Hypothesis ($ H_0 $): $ \mu \geq 1308.11 $- Alternative Hypothesis ($ H_a $): $ \mu < 1308.11 $**Option C:**- Null Hypothesis ($ H_0 $): $ \mu > 1308.11 $- Alternative Hypothesis ($ H_a $): $ \mu \leq 1308.11 $**Option D:**- Null Hypothesis ($ H_0 $): $ \mu \leq 1308.11 $- Alternative Hypothesis ($ H_a $): $ \mu > 1308.11 $**Option E:**- Null Hypothesis ($ H_0 $): $ \mu \geq 1280 $- Alternative Hypothesis ($ H_a $): $ \mu < 1280 $**Option F:**- Null Hypothesis ($ H_0 $): $ \mu \geq 1280 $- Alternative Hypothesis ($ H_a $): $ \mu < 1280 $**Task:**Calculate the standardized test statistic.**Solution:**The standardized test statistic is [enter value here].*(Round to two decimal places as needed.)*This exercise requires you to determine which hypothesis test to use and calculate the test statistic based on the given data. Understanding these steps is crucial for statistical analysis.

The summary of statistics is, x¯=1308.11,σ=196.31,n=200,μ=1280

Answered: Calculate the standardized test…

Math

Statistics

Calculate the standardized test statistic. The standardized test statistic is (Round to two decimal places as needed.)

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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Question

**Hypothesis Testing: Population Mean**

**Context:**
Use technology to help you test the claim about the population mean, $ \mu $, at the given level of significance, $ \alpha $, using the given sample statistics. Assume the population is normally distributed.

**Claim:**
\[ \mu \geq 1280 \]

- Significance level, $ \alpha = 0.07 $
- Population standard deviation, $ \sigma = 196.31 $
- Sample statistics: $ \bar{x} = 1308.11 $, $ n = 200 $

**Hypotheses Options:**

**Option A:** (Selected)
- Null Hypothesis ($ H_0 $): $ \mu \leq 1280 $
- Alternative Hypothesis ($ H_a $): $ \mu > 1280 $

**Option B:**
- Null Hypothesis ($ H_0 $): $ \mu \geq 1308.11 $
- Alternative Hypothesis ($ H_a $): $ \mu < 1308.11 $

**Option C:**
- Null Hypothesis ($ H_0 $): $ \mu > 1308.11 $
- Alternative Hypothesis ($ H_a $): $ \mu \leq 1308.11 $

**Option D:**
- Null Hypothesis ($ H_0 $): $ \mu \leq 1308.11 $
- Alternative Hypothesis ($ H_a $): $ \mu > 1308.11 $

**Option E:**
- Null Hypothesis ($ H_0 $): $ \mu \geq 1280 $
- Alternative Hypothesis ($ H_a $): $ \mu < 1280 $

**Option F:**
- Null Hypothesis ($ H_0 $): $ \mu \geq 1280 $
- Alternative Hypothesis ($ H_a $): $ \mu < 1280 $

**Task:**
Calculate the standardized test statistic.

**Solution:**
The standardized test statistic is [enter value here].

*(Round to two decimal places as needed.)*

This exercise requires you to determine which hypothesis test to use and calculate the test statistic based on the given data. Understanding these steps is crucial for statistical analysis.

Expert Solution

Step 1

The summary of statistics is,

$\bar{x} = 1308.11, σ = 196.31, n = 200, μ = 1280$

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