Question

A teacher claims that the proportion of students expected to pass an exam is greater than 80%. To test this claim, the teacher administers the test to 200 random students and determines that 151 students pass the exam. The following is the setup for this hypothesis test: {H0:p=0.80 Ha:p>0.80 Find the test statistic for this hypothesis test for a proportion. Round your answer to 2 decimal places.

Provide your answer below: $$

test statistic:

Answer 1

z=-1.591

Explanation:

Null Hypotheses,

`H_0 : p=0.8\\H_a: p>0.80`

So we use z-test for one population proportion (right-tailed test)

According to this informaton, we defined that

`\alpha=0.05`

`z_c=1.64` (critical value)

So our Rejection region is
`R={z:z>1.64}`

`z=\frac{\bar{p}-p_0}{√(p_0(1-p_0)/n)} = (0.755-0.8)/(√(0.8(1-0.8)/200))=-1.591`

Not rejection.