A study of students taking Statistics 101 was done. Four hundred students who studied for more than 10 hours averaged a B. Two hundred students who studied for less than 10 hours averaged a C. This difference was significant at the 0.01 level. What does this mean?
a study of students taking Statistics 101 was done Four hundred students who studied for more than 10 hours ave. a B. Two hundred students who studied for less than 10 hr. ave. a C. The difference was significant at the 0.01 level. what does this mean?
In statistics, the significance level, often denoted as alpha (α), represents the probability of rejecting the null hypothesis when it is true. In your question, it states that the difference in average grades between students who studied for more than 10 hours and those who studied for less than 10 hours was significant at the 0.01 level. This means that the probability of observing such a difference (or an even more extreme difference) due to chance alone is less than or equal to 0.01, assuming that there is no real difference between the two groups.
To determine the significance level and assess the statistical significance of this result, a hypothesis test was likely performed. Here are the steps involved:
1. Formulating the null hypothesis (H0) and alternative hypothesis (Ha):
- Null hypothesis (H0): There is no difference in average grades between students who studied for more than 10 hours and those who studied for less than 10 hours.
- Alternative hypothesis (Ha): There is a difference in average grades between students who studied for more than 10 hours and those who studied for less than 10 hours.
2. Choosing the significance level (α): In this case, the significance level was set to 0.01, which means that we are willing to accept a 1% chance of making a Type I error - rejecting the null hypothesis when it is actually true.
3. Collecting and analyzing the data: The researchers gathered data from 400 students who studied for more than 10 hours and 200 students who studied for less than 10 hours. They then calculated the average grades for each group.
4. Conducting a statistical test: The specific statistical test used to compare the two groups' average grades was likely a t-test or a z-test, depending on the assumptions and characteristics of the data.
5. Determining the p-value: The p-value is a measure of the evidence against the null hypothesis. It represents the probability of observing a test statistic (or more extreme) under the assumption that the null hypothesis is true. In this case, the observed difference in average grades between the two groups resulted in a p-value less than or equal to 0.01.
6. Drawing conclusions: Since the p-value is less than the significance level (α = 0.01), the researchers rejected the null hypothesis. This means that there is strong evidence to suggest that there is a significant difference in average grades between students who studied for more than 10 hours and those who studied for less than 10 hours.
In summary, the statement that the difference in average grades between students who studied for more than 10 hours and those who studied for less than 10 hours was significant at the 0.01 level means that the observed difference in average grades is unlikely to occur by chance alone. It provides evidence to support the conclusion that there is a real difference in performance based on the number of study hours.