Question

# To identify:The error in the hypothesis test.

Upper level algebra
To identify:The error in the hypothesis test.

2020-12-29
Given:
The mathematics department at one university reports that the failure rate for college algebra is no more than 35% in any given semester. A group of students believes the rate is higher, and they decided to use a hypothesis test to see if they are correct. Based on the sample they obtain, they decided to reject the null hypothesis. If, in reality, the failure rate is 34%.
Definition:
Types of errors:
1. Rejecting a true null hypothesis is called a Type I error.
2. Failing to reject a false null hypothesis is called a Type II error.
Calculation:
Let us write the null and alternative hypothesis to identify the type of error.
The mathematics department at one university reports that the failure rate for college algebra is no more than 35% in any given semester.
A group of students believes the rate is higher, and they decided to use a hypothesis test.
Therefore the alternative hypothesis is $$H_{\alpha} : p > 0.35$$
The opposite is the null hypothesis, $$H_{0} : p \leq 0.35$$
After performing the test, they decide to reject the null hypothesis.
Therefore the alternative hypothesis is accepted.
Itis given that in reality, the failure rate is 34%.
That is the null hypothesis is true.
Thus the students have rejected the true null hypothesis and so they have committed Type I error.
Final statement.
Yes,the students have commited Type I error.