Math Problem Statement
Give me independent t test data to solve
Solution
Here’s a set of data you can use for solving an independent t-test problem:
Problem Statement:
Two different teaching methods are being tested for their effectiveness in improving student test scores. A sample of 10 students is selected from each group, and their scores on a standardized test are recorded. The data for both groups is as follows:
Group 1 (Traditional Teaching Method):
Student | Score |
---|---|
1 | 82 |
2 | 90 |
3 | 85 |
4 | 88 |
5 | 79 |
6 | 84 |
7 | 87 |
8 | 91 |
9 | 83 |
10 | 89 |
Group 2 (New Teaching Method):
Student | Score |
---|---|
1 | 75 |
2 | 78 |
3 | 74 |
4 | 82 |
5 | 80 |
6 | 76 |
7 | 77 |
8 | 79 |
9 | 73 |
10 | 81 |
Hypothesis:
- Null Hypothesis (H₀): There is no significant difference in the average test scores between the two teaching methods.
- Alternative Hypothesis (H₁): There is a significant difference in the average test scores between the two teaching methods.
You are asked to:
- Perform an independent t-test to determine if there is a statistically significant difference in the mean test scores between the two groups.
- Use a significance level of 0.05.
Would you like to proceed with solving this t-test, or would you like additional guidance or clarification on how to approach it?
Here are some related questions:
- What is the formula for calculating the independent t-test?
- How do you calculate the degrees of freedom for an independent t-test?
- What assumptions are made in an independent t-test?
- How do you interpret the p-value from an independent t-test?
- What is the difference between a one-tailed and two-tailed t-test?
Tip: Remember to check the assumptions of the t-test, particularly the assumption of equal variances between the two groups, before proceeding with the test.
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Math Problem Analysis
Mathematical Concepts
Statistics
Hypothesis Testing
Independent T-Test
Formulas
t = (X̄1 - X̄2) / √[(s1^2/n1) + (s2^2/n2)]
Degrees of freedom: df = n1 + n2 - 2
Theorems
Central Limit Theorem
T-Distribution Properties
Suitable Grade Level
Grades 11-12, Undergraduate
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Independent Samples t-Test Example: Comparing Two Teaching Methods
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