Analyzing Academic Success?

📌 CONCEPT: One can use hypothesis testing to determine if the difference in the average marks of the students of school A and school B could be due to a genuine difference in their performance or due to the difference in the number of students in the two schools.

📐 RULE / FORMULA: If the sample sizes of the two groups are sufficiently large, one can use the z-test formula to find the z-score, which can be used to determine the p-value.

💡 WORKED EXAMPLE: Suppose the average marks of school A and school B are 85 and 80, respectively, with a difference of 5 marks. If there are 50 students in school A and 30 students in school B, we can use the z-test formula to find the z-score and determine if the difference in the average marks is statistically significant.

⚠️ COMMON MISTAKE: Students often ignore the assumption of large sample sizes or fail to check the conditions for the z-test, leading to incorrect conclusions.