Math Problem Statement
Step 2 of 5 :
Find the value of the standard deviation of the paired differences. Round your answer to one decimal place.
Solution
It seems like I can’t do more advanced data analysis right now. Please try again later. However, you can manually compute the standard deviation of the paired differences using the following steps:
- Calculate the differences between each pair of scores.
- Find the mean of these differences.
- Subtract the mean from each difference and square the result.
- Sum all the squared results.
- Divide the sum by the number of pairs minus one (this is for the sample standard deviation).
- Finally, take the square root of this result to get the standard deviation.
If you'd like, I can guide you through each step in more detail. Would you like assistance on this?
Here are 5 related questions:
- How is the null hypothesis set up for paired sample t-tests?
- What does the standard deviation represent in this context?
- How would you interpret a p-value in this hypothesis test?
- Why do we assume the differences are normally distributed?
- What impact does the significance level (α = 0.01) have on the conclusion?
Tip: Always check for normality of the differences when conducting paired sample tests, especially with small sample sizes.
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Math Problem Analysis
Mathematical Concepts
Statistics
Paired Sample T-Test
Standard Deviation
Formulas
Difference = Score(new design) - Score(old design)
Sample mean: Mean difference = (sum of differences) / n
Sample standard deviation: s = sqrt[ (Σ(d_i - mean_difference)^2) / (n - 1) ]
Theorems
Central Limit Theorem
Normal Distribution Assumption
Suitable Grade Level
College Level / Advanced High School
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