The best guess for the true difference in population means, calculated as $\bar{x}_1 - \bar{x}_2$.

The amount added and subtracted from the point estimate to create the confidence interval.

If sample sizes are at least 30 (n ≥ 30), the sampling distributions will be approximately normal.

When sampling without replacement, the sample size should be less than 10% of the population size.

The value from the t-distribution used in calculating the margin of error, based on the confidence level and degrees of freedom.

Random sampling ensures that the sample is representative of the population, reducing bias and allowing for valid inferences.

Random assignment ensures that any observed differences between treatment groups are due to the treatment itself, rather than confounding variables.

If we were to take many samples and construct 95% confidence intervals, about 95% of those intervals would contain the true difference in population means.

Increasing the sample size decreases the width of the confidence interval, providing a more precise estimate of the population parameter.

It suggests that there is no significant difference between the means of the two populations, as zero is a plausible value for the difference.

$\bar{x}_1 - \bar{x}_2$

$t^* \times \sqrt{\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2}}$

Point Estimate ± Margin of Error

Use a conservative estimate by taking the smaller of $n_1 - 1$ and $n_2 - 1$.

$(\bar{x}_1 - \bar{x}_2) \pm t^* \times \sqrt{\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2}}$