Question

Historically, the proportion of students entering a university who finished in 4 years or less was 63%. To test whether this proportion has decreased, 114 students were examined and 51% had finished in 4 years or less. To determine whether the proportion of students who finish in 4 year or less has statistically significantly decreased (at the 5% level of signficance), what is the critical value

Answer 1

z(c) = - 1,64

We reject the null hypothesis

Explanation:

We need to solve a proportion test ( one tail-test ) left test

Normal distribution

p₀ = 63 %

proportion size p = 51 %

sample size n = 114

At 5% level of significance α = 0,05, and with this value we find in z- table z score of z(c) = 1,64 ( critical value )

Test of proportion:

H₀ Null Hypothesis p = p₀

Hₐ Alternate Hypothesis p < p₀

We now compute z(s) as:

z(s) = ( p - p₀ ) / √ p₀q₀/n

z(s) =( 0,51 - 0,63) / √0,63*0,37/114

z(s) = - 0,12 / 0,045

z(s) = - 2,66

We compare z(s) and z(c)

z(s) < z(c) - 2,66 < -1,64

Therefore as z(s) < z(c) z(s) is in the rejection zone we reject the null hypothesis