Assume that you want to test the claim that the paired sample data come from a population for which the mean difference is μd = 0. 

x / 4 4 4 2 1
y / 8 9 10 9 12
Compute the absolute value of the test statistic. (Round your answer to nearest hundredth. Hint: The correct test statistic is positive.)

Assume that you want to test the claim that the paired sample data come from a population for which the mean difference is μd = 0. 

x / 4 4 4 2 1
y / 8 9 10 9 12
Compute the absolute value of the test statistic. (Round your answer to nearest hundredth. Hint: The correct test statistic is positive.)

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import numpy as np
from scipy.stats import t

# Given data
x = np.array([4, 4, 4, 2, 1])
y = np.array([8, 9, 10, 9, 12])

# Calculate the differences
differences = x - y

# Calculate mean and standard deviation of differences
mean_diff = np.mean(differences)
std_diff = np.std(differences, ddof=1)

# Number of pairs
n = len(differences)

# Calculate the t-statistic
t_statistic = mean_diff / (std_diff / np.sqrt(n))

# Compute absolute value of the test statistic
abs_t_statistic = abs(t_statistic)
abs_t_statistic5.4621988647756295.462198864775629successThe absolute value of the test statistic is approximately **5.46**.

Would you like me to explain the steps further or analyze the results in more depth?

Here are five related questions for further exploration:
1. How is the t-statistic calculated, and why is it important in hypothesis testing?
2. What does the null hypothesis μd = 0 represent in this test?
3. How does the standard deviation of the differences influence the t-statistic?
4. What would the critical t-value be for a specific confidence level with this sample size?
5. How do paired sample t-tests differ from independent sample t-tests?

**Tip:** Always verify the assumptions of normality or sample size adequacy when conducting t-tests.

Assume that you want to test the claim that the paired sample data come from a population for which the mean difference is μd = 0. 

x / 4 4 4 2 1
y / 8 9 10 9 12
Compute the absolute value of the test statistic. (Round your answer to the nearest hundredth. Hint: The correct test statistic is positive.)

Learn how to compute the absolute value of the test statistic for a paired sample t-test, testing the claim that the mean difference is μd = 0. Includes step-by-step calculations for x = [4, 4, 4, 2, 1] and y = [8, 9, 10, 9, 12], using the t-statistic formula.

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