A school principal is trying to determine whether average math scores at her sch

Question

A school principal is trying to determine whether average math scores at her school exceed the state-mandated proficiency level in math. She doesn't want to subject every student to testing, so she randomly selects 25 students and gives them a standardized math test; a score of 75 represents proficiency. Her 25 students have an average score of 77, with a 95% confidence interval of (74.2, 79.8).
a. Identify the population and sample in this situation.
b. Interpret the 95% confidence interval.
c. How do you advise the principal regarding the answer to her question?
d. How would a 99% confidence interval compare to the 95% confidence interval, with regards to its center and width?

Explanation / Answer

a. The population is the students of the school. Sample is the 25 students selected randomly.

b.The 95% confidence interval is (74.2, 79.8). This interval contains the required score 75 for proficiency. There is 95% chance that the population average of mathematics test score of the school will lie in this interval.

c. It is advised to the principal to increase the sample size of the students to be tested to reduce the standard error and to get more accurate inferences about the population parameters.

d.The center of the 95% and 99% confidence intervals will be same. They differ in the widths only. A 99% confidence interval will have more width than the 95% confidence interval as a higher confidence level interval should have more width such that the population parameter will lie in the specified interval.

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