Math Problem Statement
Identify the P-value.
Solution
The image describes a hypothesis test where:
- The null hypothesis is that the mean body temperature .
- The alternative hypothesis is that (a one-tailed test).
- The sample size is .
- The test statistic is .
- The significance level is .
To find the P-value for this one-tailed t-test, we use the degrees of freedom .
Next, we can calculate the P-value using the t-distribution with 4 degrees of freedom, by looking up the t-score of 1.567 or using a calculator.
Let me compute the P-value for you.The P-value for the given hypothesis test is approximately 0.0961.
Since the P-value (0.0961) is greater than the significance level , we fail to reject the null hypothesis. This means that the data does not provide strong enough evidence to support the claim that the mean body temperature is greater than .
Do you have any questions, or would you like further details?
Here are five related questions for you:
- What is the importance of the P-value in hypothesis testing?
- How do we interpret the result if the P-value is less than the significance level?
- What are the consequences of rejecting the null hypothesis when it is true (Type I error)?
- Why is a one-tailed test used in this scenario?
- How does the sample size affect the degrees of freedom and the test outcome?
Tip: Always ensure to check the assumptions of the t-test, such as normality, especially with small sample sizes.
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Math Problem Analysis
Mathematical Concepts
Hypothesis Testing
T-distribution
Significance Level
Formulas
t = (x̄ - μ) / (s / √n)
Degrees of freedom = n - 1
Theorems
T-distribution Theorem
Suitable Grade Level
College-level Statistics
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