Asked by Brian Dykstra on Jul 11, 2024
Verified
In 2009,the average final exam score for students in an introductory math course was 72%.Five years later,a teacher wants to perform a hypothesis test to determine whether the average score of students the course has changed from the 2009 mean of 72%.The hypotheses are: H0: μ = 72%
HA: μ ≠ 72%
Explain the result of a Type I error.
A) The teacher will conclude that the average final exam score in the course has decreased when in fact it is the same.
B) The teacher will conclude that the average final exam score in the course has increased when in fact it is the same.
C) The teacher will conclude that the average final exam score in the course is the same when in fact it is the same.
D) The teacher will conclude that the average final exam score in the course is different when in fact it is the same.
E) The teacher will conclude that the average final exam score in the course is the same when in fact it is different.
Type I Error
The incorrect rejection of a true null hypothesis, also known as a "false positive."
Hypothesis Test
A method in statistics used to determine whether there is enough evidence in a sample of data to infer that a certain condition holds true for the entire population.
Average Final Exam Score
The mean score of students' final exams, providing a measure of performance at the end of a course.
- Differentiate between errors of Type I and Type II in the context of hypothesis evaluation.
Verified Answer
JM
Jesus MarquezJul 13, 2024
Final Answer :
D
Explanation :
A Type I error occurs when the null hypothesis (H0) is rejected when it is actually true. In this scenario, rejecting H0 means concluding that the average score has changed (either increased or decreased) when in reality, it has not changed from 72%.
Learning Objectives
- Differentiate between errors of Type I and Type II in the context of hypothesis evaluation.