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i need help finding the t test of the following data

To perform a t-test, we need to compare the means of two sets of data. The image you provided includes data for Olympic record times in the men's 100 meters from two different time periods: 1908-1948 and 1952-2016.

Here are the steps to perform an independent two-sample t-test:

1. **Extract the data for both groups**:
   - **1908-1948:** 10.8, 11.0, 10.6, 10.8, 11.0, 10.6, 10.8, 11.0
   - **1952-2016:** 10.3, 10.5, 9.9, 10.3, 9.9, 9.8, 9.9, 10.3

2. **Calculate the means and standard deviations of both groups**.

3. **Calculate the t-statistic**.

4. **Determine the p-value to assess the significance**.

Let's proceed with these calculations.The results of the independent two-sample t-test are as follows:

- **t-statistic:** 6.448
- **p-value:** \(1.527 \times 10^{-5}\)

### Interpretation
The p-value is extremely small, indicating that there is a significant difference between the two groups' means. This suggests that the Olympic record times in the men's 100 meters significantly improved from the period 1908-1948 to 1952-2016.

Would you like further details on this test or any other related questions?

Here are some related questions:
1. What assumptions does the independent two-sample t-test require?
2. How do we interpret the p-value in a t-test?
3. Can we conclude causation from the results of this t-test?
4. What is the effect size, and how can we calculate it from the data?
5. How does the sample size affect the t-test results?
6. What are the potential limitations of using a t-test in this context?
7. How could we visually represent the differences in the data sets?
8. What other statistical tests could be used to compare these groups?

**Tip:** When performing statistical tests, it's essential to check if the data meets the test's assumptions, such as normality and homogeneity of variance.

Learn how to perform an independent two-sample t-test on men's 100m Olympic record times from different time periods (1908-1948 and 1952-2016). Calculate the t-statistic and interpret the results, indicating significant improvement over time.

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