Question

A Pre-School teacher has created a new curriculum for teaching students new words. The new curriculum is denoted as curriculum A and the original curriculum is denoted as curriculum B. The teacher instructs one class under curriculum A and a separate class under curriculum B. The number of new words each student learns is recorded and the teacher constructs a confidence interval for: u_a-ub. The 95% t-confidence interval obtained is (1.26, 4.78).

(i) Based on the confidence interval the teacher constructed, do students learn the same number of words on average under curriculums A and B? Explain how you reached your conclusion. (ii) Interpret the confidence interval in words.

(iii) What requirements are needed for the above confidence interval to be valid?

Answer 1

(i) The 95% confidence interval is (1.26, 4.78) for u_a-u_b. Since 0 does not lie in this confidence interval, we can conclude that the students learn more numbers of words on an average under curriculum A then they do under curriculum B. In other words students do not learn the same number of words on average under curriculum A and B. Since 0 does not lie in the given confidence interval we can say with 95% certainty that u_a>u_b

(ii) We can be 95% confident that the true mean difference between the average number of words learned under curriculum A and the average number of words learned under curriculum B lies between 1.26 and 4.78

(iii)

The following conditions must have been met:

• Randomization: The sample students must be selected randomly from the both the classes.
• Independent : The sample students number of words learnt must be independent of other students number of words learnt and must only be based on the teachers teachings of the curriculum.