Question

Match the following scenarios with the correct interpretations. A confidence interval for the difference between two means contains zero.

There is not evidence of a difference in the averages of the first and second paired measurements. It is plausible that the two means are equal, and therefore there is not evidence of a difference. There is evidence that the average of the second measurement is greater than the average of the first measurement. It is plausible that the two means are equal, and therefore there is evidence of a difference. It is not plausible that the two means are equal, and therefore there is evidence of a difference. It is not plausible that the two means are equal, and therefore there is not evidence of a difference. There is evidence that the average of the first measurement is greater than the average of the second measurement.

A confidence interval for the difference between two means does not contain zero.

There is not evidence of a difference in the averages of the first and second paired measurements. It is plausible that the two means are equal, and therefore there is not evidence of a difference. There is evidence that the average of the second measurement is greater than the average of the first measurement. It is plausible that the two means are equal, and therefore there is evidence of a difference. It is not plausible that the two means are equal, and therefore there is evidence of a difference. It is not plausible that the two means are equal, and therefore there is not evidence of a difference. There is evidence that the average of the first measurement is greater than the average of the second measurement.

A confidence interval for the average paired difference is entirely negative.

There is not evidence of a difference in the averages of the first and second paired measurements. It is plausible that the two means are equal, and therefore there is not evidence of a difference. There is evidence that the average of the second measurement is greater than the average of the first measurement. It is plausible that the two means are equal, and therefore there is evidence of a difference. It is not plausible that the two means are equal, and therefore there is evidence of a difference. It is not plausible that the two means are equal, and therefore there is not evidence of a difference. There is evidence that the average of the first measurement is greater than the average of the second measurement.

A confidence interval for the average paired difference is entirely positive.

There is not evidence of a difference in the averages of the first and second paired measurements. It is plausible that the two means are equal, and therefore there is not evidence of a difference. There is evidence that the average of the second measurement is greater than the average of the first measurement. It is plausible that the two means are equal, and therefore there is evidence of a difference. It is not plausible that the two means are equal, and therefore there is evidence of a difference. It is not plausible that the two means are equal, and therefore there is not evidence of a difference. There is evidence that the average of the first measurement is greater than the average of the second measurement.

Answer 1

A confidence interval containing zero suggests no significant difference between two means, while a confidence interval not containing zero shows a significant difference, with the direction of the interval indicating whether the first or second measurement's average is greater.

Step-by-step explanation:

When analyzing the scenarios provided, one must consider the interpretation of confidence intervals in the context of statistical hypothesis testing. For a confidence interval that contains zero, it indicates that the difference between two means is not statistically significant, suggesting that it is plausible that the two means are equal. This outcome does not provide evidence of a difference between the measurements. Therefore, the correct interpretation is 'It is plausible that the two means are equal, and therefore there is not evidence of a difference.'

Conversely, if a confidence interval for the difference between two means does not contain zero, it suggests that there is a significant difference between the two means, and it is not plausible that they are equal. Thus, the second measurement could be greater than the first, or vice versa, depending on the confidence interval's direction. If the interval is entirely negative, there is evidence that the average of the first measurement is greater than the second. If the interval is entirely positive, then there is evidence that the average of the second measurement is greater than the first.