STATS PART B

What does the value of b₁ represent in this context?

The average change in heart pumping capacity was +7.833 units more in the ESC group than in the control group.

What α-level is being used in this analysis? How do you know?

α = 0.01. This is identified because the fill argument in gf_histogram() shades the middle 99% of the distribution, leaving 0.5% in each tail as the unlikely region.

Locate the center of the sampling distribution and explain its significance.

The distribution is centered at approximately 0, representing the assumption of the null hypothesis (β₁ = 0). Under the null, the average shuffled group mean difference should equal 0.

What conclusion should be drawn about the null hypothesis?

Reject the null hypothesis because p = 0.001 < α = 0.01, indicating that results are statistically significant.

If only 10 sheep were used but b₁ stayed at +7.833, what would happen to the p-value?

The p-value would increase. Fewer sheep result in a larger standard error, wider sampling distribution, and a higher proportion of shuffled b₁ values exceeding ±7.833.