... individual would lose on the Atkins plan, but we can be 95% confident that the average difference lies between 1.7 and 15.2 pounds. The difference μAμC might plausibly be any value inside the interval. In particular, the break-even value 5 pounds lies inside the confidence interval and is a plausible value for the difference between the population means.

Table 17.3 Numerical summary of a two-sample t-interval.

Difference 8.41
Std Err Difference 3.37
Degrees of Freedom 60.83
95% Confidence Interval 1.68 to 15.16

Because 0 is not in this interval, the means are statistically significantly different from each other. We would say “Dieters on the Atkins diet lost statistically significantly more weight on average than those on the conventional ...

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