https://file.aiquickdraw.com/mathbot/file/1726362749784363py8jl.jpg

An SAT prep course claims to increase student scores by more than 6060 points, on average. To test this claim, 99 students who have previously taken the SAT are randomly chosen to take the prep course. Their SAT scores before and after completing the prep course are listed in the following table. Test the claim at the 0.050.05 level of significance assuming that the population distribution of the paired differences is approximately normal. Let scores before completing the prep course be Population 1 and let scores after completing the prep course be Population 2. Compute the value of the test statistic. Round your answer to three decimal places

The value of the test statistic is approximately \( t = 4.402 \), rounded to three decimal places.

Would you like more details or have any other questions? Here are 5 related questions to further explore this topic:

1. How is the t-distribution used to determine significance in hypothesis testing?
2. What are the critical t-values for different degrees of freedom?
3. How can confidence intervals be constructed based on this test?
4. What assumptions must be met for a paired t-test to be valid?
5. How does increasing sample size affect the reliability of the t-test?

**Tip:** Always check that the paired differences follow a roughly normal distribution when performing a paired t-test.

An SAT prep course claims to increase student scores by more than 60 points, on average. To test this claim, 9 students who have previously taken the SAT are randomly chosen to take the prep course. Their SAT scores before and after completing the prep course are listed in the following table. Test the claim at the 0.05 level of significance assuming that the population distribution of the paired differences is approximately normal. Let scores before completing the prep course be Population 1 and let scores after completing the prep course be Population 2. Compute the value of the test statistic. Round your answer to three decimal places.

Test the claim that an SAT prep course increases scores by more than 60 points using a paired t-test. Includes SAT scores for 9 students before and after taking the course, the 0.05 significance level, and the computed test statistic.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation