Astatistics teacher taught a large introductory statistics class, with 500 students having enrolled over many years. the mean score over all those students on the first midterm was =78 with standard deviation =10 . one year, the teacher taught a much smaller class of only 25 students. the teacher wanted to know if teaching a smaller class was more effective and students performed better. we can consider the small class as an srs of the students who took the large class over the years. the average midterm score was x¯=83 . the hypothesis should be:

Step-by-step explanation:

Given that a statistics teacher taught a large introductory statistics class, with 500 students having enrolled over many years.

Mean = 78 and std dev =10

Next time, sample size n was reduced to 25

For smaller sample size the mean was found to be = 83

The teacher wanted to know if teaching a smaller class was more effective and students performed better

ie comparison of two means of two samples should be done with different sample sizes but same teacher.

Hence hypothesis should be:

where x denotes the I sample and Y the second with 25 students.