### T-Test for Population Mean \( \mu \) at Given Level of Significance \( \alpha \)#### Problem StatementUse a t-test to 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:** \( \mu \geq 8300 \)- **Level of Significance (\( \alpha \)):** 0.01 - **Sample Statistics:** - Sample Mean (\( \bar{x} \)): 8100 - Sample Standard Deviation (\( s \)): 460 - Sample Size (\( n \)): 21#### Step-by-step Procedure1. **Identifying Hypotheses:** - What are the null and alternative hypotheses? Select the correct option: - **A.** \( H_0: \mu \neq 8300 \) \( H_a: \mu = 8300 \) - **B.** \( H_0: \mu \leq 8300 \) \( H_a: \mu > 8300 \) - **C.** \( H_0: \mu = 8300 \) \( H_a: \mu \neq 8300 \) - **D.** \( H_0: \mu \geq 8300 \) \( H_a: \mu < 8300 \)2. **Calculate the Standardized Test Statistic:** - The standardized test statistic is \(\boxed{\phantom{0.00}}\). (Round to two decimal places as needed.)3. **Determine the P-Value:** - The P-value is \( P = \boxed{\phantom{0.000}} \). (Round to three decimal places as needed.)4. **Decide to Reject or Fail to Reject the Null Hypothesis:** - Choose the correct answer below: - **A.** Fail to reject \( H_0 \). At the 1% level of significance, there is not enough evidence to reject the claim. - **B.** Reject \( H_0 \). At the 1% level of significance, there is not enough evidence to reject the claim. - **C.** Fail to reject \( H_0 \). At the 1% level

Sample size =21Sample mean=8100Standard deviation =460

Answered: Use a t-test to test the claim about…

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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