Means

To ensure all participants receive both treatments at some point during the study period, increasing participant satisfaction levels.

To allow each participant an equal chance at choosing their preferred weight loss technique, fostering commitment.

To control all potential confounding variables simultaneously across treatment groups effectively during analysis phase only.

To minimize bias and ensure any differences observed are likely due to treatment rather than other variables or selection effects.

There is a 95% probability that the population mean difference will be exactly 7.5 units.

We are 95% confident that the true difference in population means lies between 5 and 10 units.

Every sample we take will produce a confidence interval that includes the number range from 5 to 10.

The sample data show with absolute certainty that one mean is between 5 and 10 units higher than the other.

The populations have the same mean

The sample sizes are too small to draw a valid inference

A smaller range of possible values for the difference of means

A larger range of possible values for the difference of means

When one group variance triples another’s variance.

In cases where variances within each group being compared can reasonably be assumed as equal.

When each group comes from distinctly different distributions.

When each group has exactly three times more subjects than the other.

The null hypothesis that there is no difference between the populations can be rejected at the 5% significance level.

There is a 95% probability that the true difference between population means equals zero.

The zero within the interval indicates there's no variation between individual samples.

The probability that one sample mean is greater than the other is 95%.

Mean

Standard deviation

Range

Median

Type I error

Central limit theorem

Sampling bias

Law of large numbers

There is no difference between the means of the populations being compared.

The null hypothesis cannot be rejected at the 99% confidence level.

The difference between the means is statistically significant at the 99% confidence level.

There is a strong evidence to support the alternative hypothesis at the 99% confidence level.

Two-sample t-test

Chi-square test

Binomial probability test

One-sample z-test

Misestimation leading to potentially erroneous conclusions due to inappropriate assumption of homogeneity of variances.

Reduced precision in confidence intervals which can lead to overly conservative estimates and lower statistical significance.

One inflation of Type II error owing to heightened variability within estimates that diminishes detectable effect sizes.

Diminution of power because larger sample sizes are needed to compensate for increased uncertainty in data collection.