Question

The statewide pass rates for ENGL&101 across Washington state community colleges is 68%. An instructor in the English department at CBC believes rates at CBC may be higher than the state average. This study can be stated as a formal hypothesis test in the following way:

H0 : p=0.68
HA: p > 0.68
To perform his study, he took a random sample of 250 students at CBC that had taken
ENGL&101, and found that 179 had passed the course.
Using your g from the last question, calculate the test statistic for the hypothesis test. Round your answer to two decimal places.

Answer 1

The calculated value Z=1.2413 < 1.96 at 0.05 level of significance

Null hypothesis is accepted

An instructor in the English department at CBC believes rates at CBC may be equal to the state average

Explanation:

Step(i):-

Given Population proportion

P=68%= 0.68

Sample proportion

`p^(-) =(x)/(n) = (179)/(250) = 0.716`

Null hypothesis : H₀ : p = 0.68

Alternative Hypothesis :H₁ : p > 0.68

Step(ii):-

Test statistic

`Z = \frac{p^(-)-P }{\sqrt{(P Q)/(n) } }`

`Z = \frac{0.716-0.68 }{\sqrt{(0.68 X 0.32)/(250) } }`

Z = 1.2413

Level of significance

`Z_(0.05) = 1.96`

The calculated value Z=1.2413 < 1.96 at 0.05 level of significance

Null hypothesis is accepted

An instructor in the English department at CBC believes rates at CBC may be equal to the state average