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## Statistics and probability

### Course: Statistics and probability>Unit 13

Lesson 2: Comparing two means

# Hypothesis testing in experiments

You might need: Calculator

## Problem

Researchers wanted to test whether highlighting unimportant passages in a text makes the content harder to comprehend.
They randomized a group of 300 students between a treatment group and a control group. Both groups were asked to answer a 38-point reading comprehension test. The text given to the treatment group had inappropriate passages highlighted, while the text of the control group wasn't highlighted at all.
The results of the experiment showed that the mean score of the treatment group is 8 points less than the mean score of the control group. To test whether the results could be explained by random chance, the researchers created the table below, which summarizes the results of 1000 re-randomizations of the data (with differences between means rounded to the nearest 2 points).
According to the simulations, what is the probability of the treatment group's mean being lower than the control group's mean by 8 points or more?
$\qquad$
Assume that if the probability you found is lower than 5, percent, then the result should be considered significant.
What should we conclude regarding the experiment's result?
Treatment group mean minus Control group meanFrequency
minus, 1210
minus, 1012
minus, 854
minus, 679
minus, 4108
minus, 2130
0159
2151
4127
677
847
1034
1212
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