By coincidence, two experiments with an experimental group and a control group come up with the same t value. But one is based on 100 people total, and the other is based on 10 people total. The one with only 10 people, compared to the larger experiment, will have:Question 2Answera.A larger degrees of freedomb.A smaller standard errorc.A larger p-valued.A larger average of means
Question
By coincidence, two experiments with an experimental group and a control group come up with the same t value. But one is based on 100 people total, and the other is based on 10 people total. The one with only 10 people, compared to the larger experiment, will have:Question 2Answera.A larger degrees of freedomb.A smaller standard errorc.A larger p-valued.A larger average of means
Solution
The experiment with only 10 people, compared to the larger experiment, will have a larger p-value.
Here's why:
The p-value is a measure of the probability that an observed difference could have occurred just by random chance. The smaller the p-value, the greater the statistical significance of the observed difference.
In an experiment with a smaller sample size (like the one with 10 people), the variability is likely to be higher because there are fewer data points to represent the population. This higher variability can make it harder to detect a true effect, if one exists. As a result, the p-value is likely to be larger, indicating a lower level of statistical significance.
So, the correct answer is c. A larger p-value.
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