Answer:
To determine whether the difference in mean reaction times between the loud-music group and the silent group is likely due to chance or if there is evidence that music has an effect on reaction time, a statistical analysis is needed. One way to do this is by performing a hypothesis test.
Here's how you can approach the analysis:
Null Hypothesis (H0): There is no significant difference in reaction times between the loud-music group and the silent group. In other words, the music does not have an effect on reaction time.
Alternative Hypothesis (H1): There is a significant difference in reaction times between the two groups. The music has an effect on reaction time.
Next, you can conduct a t-test for the difference in means of independent samples. You can use the means and standard deviations from the combined data to calculate a t-statistic. The t-statistic measures the difference in means relative to the variability in the data.
Then, you can calculate the p-value associated with the t-statistic. If the p-value is small (typically below a significance level like 0.05), you can reject the null hypothesis in favor of the alternative hypothesis. This would indicate that the difference in reaction times is likely not due to chance and that there is evidence that the music has an effect on reaction time.
However, the results of the t-test should be interpreted in the context of the specific data and study design. If the p-value is not small, it suggests that the observed difference in means could reasonably occur due to random sampling variability.
In summary, a hypothesis test with appropriate data analysis can provide insights into whether the difference in reaction times is likely due to chance or if there is evidence of an effect from listening to loud music. The decision will depend on the p-value obtained from the analysis.
Explanation:
To determine whether the difference in mean reaction times between the loud-music group and the silent group is likely due to chance or if there is evidence that the music has an effect on reaction time, we can perform a statistical analysis. One common method to assess this is to conduct a paired t-test or a similar hypothesis test. However, in this case, you provided a series of differences in means (mean of group 1 - mean of group 2) that were calculated based on random samples of 25 students from the combined dataset.
We can use these differences to assess whether the observed difference is statistically significant. To do this:
Calculate the mean and standard deviation of the differences in means.
Perform a t-test or a similar hypothesis test to determine if the observed differences are significantly different from zero.
If the p-value obtained from the test is less than a chosen significance level (e.g., 0.05), then we can conclude that the difference in mean reaction times between the two groups is statistically significant, suggesting that the music has an effect on reaction time.
Without the actual values of the differences and the standard deviations, it's not possible to perform the calculations and provide a definitive conclusion. You would need to perform these statistical calculations using a software tool or statistical calculator.
The key point is that by comparing the differences in means to zero and conducting a hypothesis test, you can determine if the observed differences are likely due to chance or if there's evidence of an effect from the music on reaction time.