Question

A statistics 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:

Answer 1

The hypothesis for the teacher's question is whether teaching a smaller class was more effective and students performed better. The hypothesis should be tested using a one-sample t-test.

Step-by-step explanation:

The hypothesis for the teacher's question would be:

H0: There is no significant difference in the mean midterm scores between the large introductory statistics class and the smaller class.

Ha: The mean midterm scores of the smaller class are higher than the large introductory statistics class.

To test this hypothesis, the teacher can use a one-sample t-test. The teacher should calculate the test statistic, which is the difference between the sample mean of the smaller class and the population mean of the large class, divided by the standard deviation of the sample mean.

If the test statistic is significantly different from zero, the teacher can reject the null hypothesis and conclude that the smaller class performed better.

Answer 2

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:

`H_0: \bar x =\bar y\\H_a : \bar x <\bar Y`

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