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Making the correct decision

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

In this example, the p-value was determined to be 0.944.

Come to a conclusion and interpret the results for this hypothesis test for a proportion (use a significance level of 5%)

Select the correct answer below:

 

The decision is to fail to reject the Null Hypothesis.
The conclusion is that there is not enough evidence to support the claim.

Answer Explanation

Correct answer:

The decision is to fail to reject the Null Hypothesis.
The conclusion is that there is not enough evidence to support the claim.

To come to a conclusion and interpret the results for a hypothesis test for proportion using the P-Value Approach, the first step is to compare the p-value from the sample data with the level of significance.

The decision criteria is then as follows:

If the p-value is less than or equal to the given significance level, then the null hypothesis should be rejected.

So, if p≤α, reject H0; otherwise fail to reject H0.

When we have made a decision about the null hypothesis, it is important to write a thoughtful conclusion about the hypotheses in terms of the given problem's scenario.

Assuming the claim is the null hypothesis, the conclusion is then one of the following:

  • if the decision is to reject the null hypothesis, then the conclusion is that there is enough evidence to reject the claim.
  • if the decision is to fail to reject the null hypothesis, then the conclusion is that there is not enough evidence to reject the claim.

Assuming the claim is the alternative hypothesis, the conclusion is then one of the following:

  • if the decision is to reject the null hypothesis, then the conclusion is that there is enough evidence to support the claim.
  • if the decision is to fail to reject the null hypothesis, then the conclusion is that there is not enough evidence to support the claim

 

In this example the p-value = 0.944.  We then compare the p-value to the level of significance to come to a conclusion for the hypothesis test.

In this example, the p-value is greater than the level of significance which is 0.05.

Since the p-value is greater than the level of significance, the conclusion is to fail to reject the null hypothesis.

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