A researcher reports that "Students were randomly assignment to intervention or a control group; the two groups did not differ significantly prior to the start of the intervention. At the end of the study, those receiving the intervention showed statistically significant improvement (p < 0.05) in reading fluency, as compared to those in the control group." Which of the following is NOT a valid inference based on this statement.

A. We can infer that the samples come from two different populations at the end of the study.

B. We can assume that the two groups had identical means and standard deviations at the beginning of the study.

C. The probability that the two groups came from the same population was less than 5%.

D. There is about a 1 in 20 chance that the researcher is incorrectly inferring that the two groups, post-intervention, belong to different populations.

Well, you did not give any other choices but if you chose A I suspect you are correct.

The correct answer is B.

To understand why, let's break down the given information. The researcher conducted a study where students were randomly assigned to either an intervention group or a control group. Before the intervention, the two groups did not differ significantly, meaning they were comparable.

At the end of the study, the researcher found that the group receiving the intervention showed statistically significant improvement in reading fluency compared to the control group (p < 0.05).

Now let's consider each option:

A. We can infer that the samples come from two different populations at the end of the study.
This inference is valid because the significant improvement in reading fluency suggests that the intervention had an effect. Therefore, the two populations (intervention group and control group) are likely to have different characteristics post-intervention.

B. We can assume that the two groups had identical means and standard deviations at the beginning of the study.
This inference is NOT valid because the statement only mentions that the two groups did not differ significantly before the intervention. It does not provide information about their means and standard deviations being identical.

C. The probability that the two groups came from the same population was less than 5%.
This inference is valid. The statement mentions that the improvement in reading fluency was statistically significant (p < 0.05). This means the probability of observing such a difference between the two groups by chance, assuming they came from the same population, is less than 5%.

D. There is about a 1 in 20 chance that the researcher is incorrectly inferring that the two groups, post-intervention, belong to different populations.
This inference is valid because a p-value of 0.05 indicates that there is a 1 in 20 (or 5%) chance that the researcher is incorrectly inferring a difference between the two groups when, in fact, there is no real difference.

In conclusion, the correct answer is B. We cannot assume that the two groups had identical means and standard deviations at the beginning of the study.