A study of 600 college students taking statistics revealed that 54 students received the grade of A. Typically 10% of the class gets an A. The difference between this gourp of students and the expected value is not significant at the 0.05 level. What does this mean?
It is just due to chance variation.
To understand what it means that the difference between the observed proportion and the expected proportion is not significant at the 0.05 level, we need to understand the concept of statistical significance and hypothesis testing.
In hypothesis testing, we compare observed data to what we would expect to see if a null hypothesis were true. The null hypothesis in this case would be that the proportion of students receiving an A is equal to 10% (expected value). The alternative hypothesis would be that the proportion is different from 10%.
To test this hypothesis, we use statistical tests. One commonly used test in this scenario is the chi-square test. This test calculates a test statistic (chi-square value) that measures the difference between expected and observed data.
The 0.05 level mentioned refers to the significance level or alpha level, which is the threshold for determining whether the results are statistically significant. It is typically set at 0.05, meaning that if the probability of observing the data given the null hypothesis is less than 0.05, we reject the null hypothesis in favor of the alternative hypothesis.
In this case, if the difference between the observed and expected proportion is not statistically significant at the 0.05 level, it means that the data does not provide strong evidence to reject the null hypothesis. The observed proportion of 54 students receiving an A could have occurred by chance alone, and it is within the range of what we would expect to see if the proportion was 10%.
However, it's worth noting that "not statistically significant" does not necessarily mean "no difference." It means that there is not enough evidence to support the claim that the proportion is different from the expected value. It is always important to consider the context and the implications of the results before drawing conclusions.