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MATH 180 MATH180 MATH/180 Week 13_ Chapter 11 (1st half) 162.pdf

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MATH 180 MATH180 MATH/180 Week 13_ Chapter 11 (1st half) 162.pdf

Answers to Multiple-Choice Problems:
A student wants to see if the correct answers to multiplechoice problems are evenly distributed. She heard a rumor that if you don’t know the answer, youshould always pick C.
In a sample of 100 multiple-choice questions from prior tests and quizzes, thedistribution of correct answers are given in the table below. In all of these questions, there were fouroptions {A, B, C, D}.
Correct Answers (n= 100)
                 A         B            C              D
Count     12      24            33           31
The Test:Test the claim that correct answers for all multiple-choice questions are not evenly distributed. Test this claim at the 0.05 significance level.
We have proven that correct answers for all multiple-choice questions are evenlydistributed.
(a)

Description

MATH 180 MATH180 MATH/180 Week 13_ Chapter 11 (1st half) 162.pdf

Answers to Multiple-Choice Problems:
A student wants to see if the correct answers to multiplechoice problems are evenly distributed. She heard a rumor that if you don’t know the answer, youshould always pick C.
In a sample of 100 multiple-choice questions from prior tests and quizzes, thedistribution of correct answers are given in the table below. In all of these questions, there were fouroptions {A, B, C, D}.
Correct Answers (n= 100)
                 A         B            C              D
Count     12      24            33           31
The Test:Test the claim that correct answers for all multiple-choice questions are not evenly distributed. Test this claim at the 0.05 significance level.
We have proven that correct answers for all multiple-choice questions are evenly distributed.
(a) What is the null hypothesis for this test in terms of the probabilities of the outcomes?
(b) What is the value of the test statistic? Round to 3 decimal places unless yoursoftware automatically rounds to 2 decimal places.
(c) Use software to get the P-value of the test statistic. Round to 4 decimal places unlessyour software automatically rounds to 3 decimal places.
(d) What is the conclusion regarding the null hypothesis?
(e) Choose the appropriate concluding statement
Solution or Explanation
(a)We are testing whether or not the distribution of correct answers is evenly distributed. So we startby assuming all of the probabilities are equal to 1/k where kis the number of outcomes.H0: pA= pB= pC= pD= 1/4.————————-
(b)If you are not using software, the test statistic is calculated by completing the table below.If you use software, or different intermediate rounding, your answer might be slightly different thanthe one above.————————-
(c)The P-value is found using software. P-value depending on the exact value of your teststatistic.————————-
(d)We reject the null hypothesis because the P-value of the test statistic () is less than thesignificance level of .————————-
(e)We are rejecting the null hypothesis that the probabilities of all four outcomes are the same.Specifically, this supports the claim that correct answers are not evenly distributed.
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MATH 180 MATH180 MATH/180 Week 13_ Chapter 11 (1st half) 162.pdf

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