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Let’s return to the quiz question example from the previous exercise — we want to remove our quiz question from our website if the probability of a correct response is different from 70%. Suppose we collected data from 100 learners and ran a binomial hypothesis test with the following null and alternative hypotheses:

  • Null: The probability that a learner gets the question correct is 70%.
  • Alternative: The probability that a learner gets the question correct is not 70%.

Assuming that we set a significance threshold of 0.05 for this test:

  • If the p-value is less than 0.05, the p-value is significant. We will “reject the null hypothesis” and conclude that the probability of a correct answer is significantly different from 70%. This would lead us to re-rewrite the question.
  • If the p-value is greater than 0.05, the p-value is not significant. We will not be able to reject the null hypothesis, and will conclude that the probability of a correct answer is not significantly different from 70%. This would lead us to leave the question on the site.

Instructions

1.

Suppose that we ran the binomial hypothesis test described in this exercise and calculated a p-value of 0.062. Using a significance threshold of 0.05, should we remove the question from our site? Change the value of remove_question_1 to 'yes' or 'no' to indicate your answer.

2.

We ran the same hypothesis test for a different question and calculated a p-value of 0.013. Again using a significance threshold of 0.05, should we remove this question from our site? Change the value of remove_question_2 to 'yes' or 'no' to indicate your answer.

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