https://file.aiquickdraw.com/mathbot/file/1729220537047odo65nvt.jpg

The image contains a statistical problem about testing the average (mean) scores of students in Grade VIII at SMP A. The task involves using a **One-Sample T-Test** in SPSS to check if the students' average score is equal to 75.

### Key Information:
1. **Hypotheses**:
   - **Null Hypothesis (H₀)**: The average score of students is equal to 75.
   - **Alternative Hypothesis (H₁)**: The average score of students is not equal to 75.

2. **SPSS Procedure**:
   - Enter the data.
   - Perform a **One-Sample T-Test** where the test value is 75.

3. **Results** from SPSS:
   - **t-value** = 0.363
   - **Degrees of freedom (df)** = 19
   - **p-value (Sig. 2-tailed)** = 0.720
   - Since the **p-value (0.720)** is greater than 0.05, we fail to reject the null hypothesis (H₀).

4. **Conclusion**: The average score of students in Grade VIII at SMP A is not significantly different from 75.

### Additional Problem:
There is a second problem asking whether, if the standard deviation is 15.3 and the mean score is 76, the average score is significantly different from 75. This would involve using a different t-test, with a known mean and standard deviation.

Would you like a detailed breakdown of how to solve this second problem? 

### 5 Related Questions:
1. How is the **t-value** calculated in a One-Sample T-Test?
2. What are the conditions under which you reject the null hypothesis in a t-test?
3. How do you interpret confidence intervals in the context of hypothesis testing?
4. Why is the **p-value** important in hypothesis testing?
5. What changes in the conclusion if the **p-value** were less than 0.05?

#### Tip:
When performing hypothesis tests, always ensure your sample size is adequate to avoid Type I or Type II errors.

A study is conducted to test whether the average test scores of Grade VIII students at SMP A are equal to 75. SPSS is used to perform a One-Sample T-Test, with the test value being 75. The hypotheses are: Null Hypothesis (H₀): the mean score is equal to 75, and Alternative Hypothesis (H₁): the mean score is not equal to 75. The results show a t-value of 0.363 and a p-value of 0.720. Is the mean significantly different from 75?

Learn how to perform a One-Sample T-Test to determine whether the average test score of Grade VIII students is 75. Includes SPSS steps, statistical formulas, and detailed hypothesis testing. Suitable for students in Grades 11-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation