Question

For students who first enrolled in two year public institutions in a recent​ semester, the proportion who earned a​ bachelor's degree within six years was

0.394. The president of a certain college believes that the proportion of students who enroll in her institution have a higher

completion rate.

​(a)	Determine the null and alternative hypotheses.
​(b)	Explain what it would mean to make a Type I error.
​(c)	Explain what it would mean to make a Type II error.

Answer 1

a)

Claim : The proportion of students who enroll in her institution have a higher completion rate. i.e P > 0.394

Hypothesis :

Null hypothesis - H₀ : P = 0.394

Alternative hypothesis - H₁ : P > 0.394   ( Claim )

B)

When we reject true null hypothesis ( H₀) then type 1 error will be occurs .

In this example if we reject null hypothesis that the proportion who earned a​ bachelor's degree within six years was 0.394

(i.e H0: P=0.394 ) , but it is actually true then type 1 error will be occurs.

c)

When we fail to reject false null hypothesis ( H₀) then type 2 error will be occurs.

In this example if you fail to reject null hypothesis that the proportion who earned a​ bachelor's degree within six years was 0.394 (i.e H0: P=0.394 ) , but it is actually false then type 2 error will be occurs.