It has long been stated that the mean temperature of humans is 98.6°F. However, two researchers currently involved in the subject thought that the mean temperature of humans is less than 98.6°F. They measured the temperatures of 44 healthy adults 1 to 4 times daily for 3 days, obtaining 200 measurements. The sample data resulted in a sample mean of 98.2°F and a sample standard deviation of 0.9°F. Use the P-value approach to conduct a hypothesis test to judge whether the mean temperature of humans is less than 98.6°F at the a= 0.01 level of significance. State the hypotheses. H₂: ▼98.6°F H₁: 98.6°F Find the test statistic. (Round to two decimal places as needed.) The P-value is (Round to three decimal places as needed.) What can be concluded? O A. Do not reject Ho since the P-value not less than the significance level.
It has long been stated that the mean temperature of humans is 98.6°F. However, two researchers currently involved in the subject thought that the mean temperature of humans is less than 98.6°F. They measured the temperatures of 44 healthy adults 1 to 4 times daily for 3 days, obtaining 200 measurements. The sample data resulted in a sample mean of 98.2°F and a sample standard deviation of 0.9°F. Use the P-value approach to conduct a hypothesis test to judge whether the mean temperature of humans is less than 98.6°F at the a= 0.01 level of significance. State the hypotheses. H₂: ▼98.6°F H₁: 98.6°F Find the test statistic. (Round to two decimal places as needed.) The P-value is (Round to three decimal places as needed.) What can be concluded? O A. Do not reject Ho since the P-value not less than the significance level.
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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![### Understanding Hypothesis Testing in Human Body Temperature
It has long been stated that the mean temperature of humans is 98.6°F. However, two researchers currently involved in the subject believe that the mean temperature of humans is less than 98.6°F. They measured the temperatures of 44 healthy adults 1 to 4 times daily for 3 days, obtaining 200 measurements. The sample data resulted in a sample mean of 98.2°F and a sample standard deviation of 0.9°F. Use the P-value approach to conduct a hypothesis test to judge whether the mean temperature of humans is less than 98.6°F at the α = 0.01 level of significance.
### Steps in Hypothesis Testing
#### 1. State the Hypotheses:
The null hypothesis (H₀) and the alternative hypothesis (H₁) are formulated as follows:
H₀: μ = 98.6°F
H₁: μ < 98.6°F
#### 2. Find the Test Statistic:
The test statistic can be calculated using the formula for the t-score. However, specific values need to be filled in:
\[ t_0 = \ \text{(Round to two decimal places as needed.)} \]
#### 3. Calculate the P-value:
Using the test statistic, the P-value will be determined to decide whether we will reject the null hypothesis.
\[ \text{The P-value is} \ \ \text{(Round to three decimal places as needed.)} \]
### What Can Be Concluded?
A decision will be made based on the P-value and the significance level (α):
#### Options:
A. Do not reject H₀ since the P-value is not less than the significance level.
B. Reject H₀ since the P-value is less than the significance level.
By comparing the P-value to the significance level, a conclusion can be drawn regarding the hypothesis.
### Visual Explanation (if applicable)
Here, no graphs or diagrams are provided in the example image. However, if there were, they could include a bell curve illustrating the distribution of sample means, a t-distribution table, or charts depicting the hypothesis testing steps.
Such visual aids help in better understanding the process of hypothesis testing and how decisions are made based on statistical data.
### Final Thought
The key takeaway from this exercise is the ability to perform a hypothesis test by calculating the test statistic and comparing](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F07fb787c-e500-4d5f-8baa-0c79bb61382c%2F0c09130a-2f7b-4067-aa31-3e1274ebab2e%2F1spmunm_processed.png&w=3840&q=75)
Transcribed Image Text:### Understanding Hypothesis Testing in Human Body Temperature
It has long been stated that the mean temperature of humans is 98.6°F. However, two researchers currently involved in the subject believe that the mean temperature of humans is less than 98.6°F. They measured the temperatures of 44 healthy adults 1 to 4 times daily for 3 days, obtaining 200 measurements. The sample data resulted in a sample mean of 98.2°F and a sample standard deviation of 0.9°F. Use the P-value approach to conduct a hypothesis test to judge whether the mean temperature of humans is less than 98.6°F at the α = 0.01 level of significance.
### Steps in Hypothesis Testing
#### 1. State the Hypotheses:
The null hypothesis (H₀) and the alternative hypothesis (H₁) are formulated as follows:
H₀: μ = 98.6°F
H₁: μ < 98.6°F
#### 2. Find the Test Statistic:
The test statistic can be calculated using the formula for the t-score. However, specific values need to be filled in:
\[ t_0 = \ \text{(Round to two decimal places as needed.)} \]
#### 3. Calculate the P-value:
Using the test statistic, the P-value will be determined to decide whether we will reject the null hypothesis.
\[ \text{The P-value is} \ \ \text{(Round to three decimal places as needed.)} \]
### What Can Be Concluded?
A decision will be made based on the P-value and the significance level (α):
#### Options:
A. Do not reject H₀ since the P-value is not less than the significance level.
B. Reject H₀ since the P-value is less than the significance level.
By comparing the P-value to the significance level, a conclusion can be drawn regarding the hypothesis.
### Visual Explanation (if applicable)
Here, no graphs or diagrams are provided in the example image. However, if there were, they could include a bell curve illustrating the distribution of sample means, a t-distribution table, or charts depicting the hypothesis testing steps.
Such visual aids help in better understanding the process of hypothesis testing and how decisions are made based on statistical data.
### Final Thought
The key takeaway from this exercise is the ability to perform a hypothesis test by calculating the test statistic and comparing
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