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:

  1. What does a p-value represent in hypothesis testing?
  2. How do you calculate the degrees of freedom in a t-test?
  3. What happens when the p-value is less than ⍺?
  4. How is the t-statistic calculated in hypothesis testing?
  5. 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