Math Problem Statement
A research report summarizes the results of the hypothesis test by stating, "t(45) = 1.31, p > .05." If ⍺ =.05, what happened in this study? Question 19 options:
The null hypothesis was rejected
The null hypothesis was not rejected
Not enough information to determine
Solution
In this study, the null hypothesis was not rejected.
Here’s why:
- The test statistic is given as t(45) = 1.31, where 45 is the degrees of freedom (df).
- The p-value is reported as p > .05.
- The significance level (⍺) is .05.
Since the p-value is greater than the significance level (p > .05), there is not enough evidence to reject the null hypothesis. In hypothesis testing, when p > ⍺, it means the result is not statistically significant, and we fail to reject the null hypothesis.
Conclusion: The null hypothesis was not rejected.
Would you like more details on hypothesis testing or any related concepts?
Here are 5 related questions:
- What does a p-value represent in hypothesis testing?
- How do you calculate the degrees of freedom in a t-test?
- What happens when the p-value is less than ⍺?
- How is the t-statistic calculated in hypothesis testing?
- What are Type I and Type II errors in hypothesis testing?
Tip: Always check both the p-value and significance level when interpreting the results of a hypothesis test.
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Math Problem Analysis
Mathematical Concepts
Hypothesis Testing
p-Value
t-Statistic
Formulas
t = (x̄ - μ) / (s / √n)
p-value
Theorems
Null Hypothesis Significance Testing
Suitable Grade Level
College Level - Introductory Statistics
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