Means

To determine if one sample mean is equal to another sample mean.

To calculate the exact difference between two population means without error.

To prove that one population mean is larger than the other.

To estimate the difference between two population means based on sample data.

The precision of the difference estimate increases, leading to a narrower confidence interval for the difference.

The increased sample size leads to greater statistical power but does not affect the mean difference's confidence interval width.

There is no change in the precision or width of the confidence interval since variances are similar.

Decreasing the small sample size to match the larger one provides a more conservative estimate with a broader confidence interval width.

198

99

200

50

Sample sizes ($n_{1}$ and $n_{2}$)

Maximum values in both samples

Combined variance

Total sum across both samples

Larger sample sizes result in narrower confidence intervals

Larger sample sizes result in wider confidence intervals

Sample size does not affect the width of the confidence interval

The relationship depends on the shape of the population distributions

The Interval becomes narrower

The confidence level cannot be changed once sample size is set

The Interval becomes wider

There is no change to the Interval WIDTH

Level of significance chosen for analysis, while changing the level of significance affects the width of the interval, it doesn't necessarily change the necessary sample size required for accurate estimation.

Variability of the observed data, as smaller variability leads to narrower intervals requiring fewer participants to achieve desired precision.

Complexity of the analytical model used, as more complex models sometimes demand a greater number of participants to ensure the robustness of the conclusions drawn.

Presence of outliers in the dataset, as their inclusion or exclusion can dramatically affect the range of values considered typical, thereby impacting the overall estimation of margin error.

Normal distributions will result in a smaller confidence interval width regardless of sample size.

Non-normal distributions can only be used when there is no variability in sample data points.

A non-normal distribution implies that both populations must have equal variances.

Small sample sizes do not benefit from the Central Limit Theorem, hence normality ensures accurate estimation.

Make it narrower

Make it wider

Shift its center towards zero

Have no effect on its width

Both samples come from populations with non-normal distributions.

The means of both populations are known and equal.

The sample sizes must be exactly equal for both groups.

The standard deviations are assumed to be approximately equal.