Question

At a certain university, students often fail general chemistry on their first attempt. Professor Brown teaches at this university and believes that the rate of first-time failure in his general chemistry classes is greater than 20% . He samples 88 students from last semester who were first-time enrollees in general chemistry and finds that 19 of them failed his course.

ii). Compute the critical value.

Answer 1

Answer: Critical value = 1.6449

Here, we have to use one sample z test for the population proportion.

The null and alternative hypotheses for this test are given as below:

Null hypothesis: H₀: The rate of first-time failure in general chemistry classes is 20%.

Alternative hypothesis: H_a: The rate of first-time failure in general chemistry classes is greater than 20%.

H₀: p = 0.20 versus H_a: p > 0.20

This is an upper or right tailed test.

We assume

Level of significance = α = 0.05

So, required critical value for this test by using z-table is given as below:

Critical value = 1.6449