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

Answer:

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

Step-by-step explanation:

Step(i):-

Given Population proportion

                                    P=68%= 0.68

Sample proportion

                            $p^{-} =\frac{x}{n} = \frac{179}{250} = 0.716$

Null hypothesis : H₀ : p = 0.68

Alternative Hypothesis :H₁ : p > 0.68

Step(ii):-

Test statistic

                         $Z = \frac{p^{-}-P }{\sqrt{\frac{P Q}{n} } }$

                        $Z = \frac{0.716-0.68 }{\sqrt{\frac{0.68 X 0.32}{250} } }$

                       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