The Dean of a university claims that no more than 10% of the students drop out of university. She chooses a random sample of 500 students and decides that she will accept the claim only if no more than 25 of the 500 students drop out of university. In fact her claim is true - the actual percentage of students who drop out of university is 8%; nevertheless the sample had 30 students who drop out. Based on the sample data the Dean would make a ________ error.
Question 7 options:
Type I
Type II
No error is being committed
Cannot be determined
no error is being committed
Type II
To answer this question, we need to understand Type I and Type II errors in hypothesis testing.
Type I error: This occurs when we reject a true null hypothesis. In other words, we conclude that there is a significant difference or effect when there actually isn't.
Type II error: This occurs when we fail to reject a false null hypothesis. In other words, we fail to identify a significant difference or effect when there actually is.
In this scenario, the Dean claims that no more than 10% of the students drop out of university. The null hypothesis would be that the percentage of students who drop out is equal to or less than 10%. The alternative hypothesis would be that the percentage of students who drop out is greater than 10%.
The Dean decides to accept the claim only if no more than 25 out of the 500 students drop out. However, the sample data shows that 30 students drop out, which is more than 25.
Since the actual percentage of students who drop out is 8% (which is less than 10%), but the Dean incorrectly rejects the null hypothesis based on the sample data, she is making a Type I error.
Therefore, the answer is: Type I.