Question

At a certain university, 16% of students fail ge neral chemistry on their first attempt. Professor Brown teachers at this university and believe He samples 96 students from last semester who were first time enrollees in general chemistry and finds that 15 of them failed his course. Using a 0.05, can you conclude that the percentage of failures differs from 33%? s the rate of first time failure in his general chemistry class is 33%.

Answer 1

Explanation:

H0: p = 0.33

Ha: p
`\\eq` 0.33

Sample proportion
`\hat{p}` = 15 / 96 = 0.15625

Test statistics

z =
`\hat{p} -p/(sqrt( p( 1- p) / n))`

=
`[0.15625-0.33/sqrt(/frac{0.33*0.67}{96})`

= -3.62

This is test statistics value.

Critical value at 0.05 level = -1.96 , 1.96.

since test statistics falls in rejection region, we have sufficient evidence to reject H_0.

We conclude at 0.05 level that we have enough evidence to support the claim.