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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:

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Answer:

z=-1.591

Step-by-step explanation:

Null Hypotheses,

[tex]H_0 : p=0.8\\H_a: p>0.80[/tex]

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

According to this informaton, we defined that

[tex]\alpha=0.05[/tex]

[tex]z_c=1.64 [/tex] (critical value)

So our Rejection region is [tex]R={z:z>1.64}[/tex]

[tex]z=\frac{\bar{p}-p_0}{\sqrt{p_0(1-p_0)/n}} = \frac{0.755-0.8}{\sqrt{0.8(1-0.8)/200}}=-1.591[/tex]

Not rejection.

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