A random sample of 100 observations from a population with standard deviation 75 yielded a sample mean of 114. Complete parts a through c below. a. Test the null hypothesis that μ = 100 against the alternative hypothesis that μ> 100, using a = 0.05. Interpret the results of the test. What is the value of the test statistic? Z= (Round to two decimal places as needed.) Find the p-value. p-value = (Round to three decimal places as needed.) State and interpret the results of the test. SELL O A. Do not reject Ho. There is sufficient evidence to indicate that the true population mean is greater than 100 at a = 0.05. OB. Reject Ho. There is sufficient evidence to indicate that the true population mean is greater than 100 at a = 0.05. O C. Reject Ho. There is insufficient evidence to indicate that the true population mean is greater than 100 at x = 0.05. O D. Do not reject Ho. There is insufficient evidence to indicate that the true population mean is greater than 100 at x = 0.05. b. Test the null hypothesis that μ = 100 against the alternative hypothesis that μ# 100, using a = 0.05. Interpret the results of the test. What is the value of the test statistic? (Round to two decimal places as needed.) Find the p-value. p-value= (Round to three decimal places as needed.)
A random sample of 100 observations from a population with standard deviation 75 yielded a sample mean of 114. Complete parts a through c below. a. Test the null hypothesis that μ = 100 against the alternative hypothesis that μ> 100, using a = 0.05. Interpret the results of the test. What is the value of the test statistic? Z= (Round to two decimal places as needed.) Find the p-value. p-value = (Round to three decimal places as needed.) State and interpret the results of the test. SELL O A. Do not reject Ho. There is sufficient evidence to indicate that the true population mean is greater than 100 at a = 0.05. OB. Reject Ho. There is sufficient evidence to indicate that the true population mean is greater than 100 at a = 0.05. O C. Reject Ho. There is insufficient evidence to indicate that the true population mean is greater than 100 at x = 0.05. O D. Do not reject Ho. There is insufficient evidence to indicate that the true population mean is greater than 100 at x = 0.05. b. Test the null hypothesis that μ = 100 against the alternative hypothesis that μ# 100, using a = 0.05. Interpret the results of the test. What is the value of the test statistic? (Round to two decimal places as needed.) Find the p-value. p-value= (Round to three 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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![## Statistical Hypothesis Testing
A random sample of 100 observations from a population with a standard deviation of 75 yielded a sample mean of 114. Complete parts a through c below.
---
### a. Test the null hypothesis that µ = 100 against the alternative hypothesis that µ > 100, using α = 0.05. Interpret the results of the test.
#### What is the value of the test statistic?
\[ z = \_\_\_ \text{ (Round to two decimal places as needed.)} \]
#### Find the p-value.
\[ p\text{-value} = \_\_\_ \text{ (Round to three decimal places as needed.)} \]
---
#### State and interpret the results of the test.
- \( \mathbf{A.} \) Do not reject \( H_0 \). There is sufficient evidence to indicate that the true population mean is greater than 100 at \( \alpha = 0.05 \).
- \( \mathbf{B.} \) Reject \( H_0 \). There is sufficient evidence to indicate that the true population mean is greater than 100 at \( \alpha = 0.05 \).
- \( \mathbf{C.} \) Reject \( H_0 \). There is insufficient evidence to indicate that the true population mean is greater than 100 at \( \alpha = 0.05 \).
- \( \mathbf{D.} \) Do not reject \( H_0 \). There is insufficient evidence to indicate that the true population mean is greater than 100 at \( \alpha = 0.05 \).
---
### b. Test the null hypothesis that µ = 100 against the alternative hypothesis that µ ≠ 100, using α = 0.05. Interpret the results of the test.
#### What is the value of the test statistic?
\[ z = \_\_\_ \text{ (Round to two decimal places as needed.)} \]
#### Find the p-value.
\[ p\text{-value} = \_\_\_ \text{ (Round to three decimal places as needed.)} \]
---](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F50bba9ff-e92f-418a-953f-7454e9aa5e30%2F8940c937-2d3d-4b10-be6f-d7c49d31c9d0%2F7ymizm_processed.jpeg&w=3840&q=75)
Transcribed Image Text:## Statistical Hypothesis Testing
A random sample of 100 observations from a population with a standard deviation of 75 yielded a sample mean of 114. Complete parts a through c below.
---
### a. Test the null hypothesis that µ = 100 against the alternative hypothesis that µ > 100, using α = 0.05. Interpret the results of the test.
#### What is the value of the test statistic?
\[ z = \_\_\_ \text{ (Round to two decimal places as needed.)} \]
#### Find the p-value.
\[ p\text{-value} = \_\_\_ \text{ (Round to three decimal places as needed.)} \]
---
#### State and interpret the results of the test.
- \( \mathbf{A.} \) Do not reject \( H_0 \). There is sufficient evidence to indicate that the true population mean is greater than 100 at \( \alpha = 0.05 \).
- \( \mathbf{B.} \) Reject \( H_0 \). There is sufficient evidence to indicate that the true population mean is greater than 100 at \( \alpha = 0.05 \).
- \( \mathbf{C.} \) Reject \( H_0 \). There is insufficient evidence to indicate that the true population mean is greater than 100 at \( \alpha = 0.05 \).
- \( \mathbf{D.} \) Do not reject \( H_0 \). There is insufficient evidence to indicate that the true population mean is greater than 100 at \( \alpha = 0.05 \).
---
### b. Test the null hypothesis that µ = 100 against the alternative hypothesis that µ ≠ 100, using α = 0.05. Interpret the results of the test.
#### What is the value of the test statistic?
\[ z = \_\_\_ \text{ (Round to two decimal places as needed.)} \]
#### Find the p-value.
\[ p\text{-value} = \_\_\_ \text{ (Round to three decimal places as needed.)} \]
---
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