Chapter 6, Section 1-HT, Exercise 058 Is B a Good Choice on a Multiple-Choice Ex

Question

Chapter 6, Section 1-HT, Exercise 058 Is B a Good Choice on a Multiple-Choice Exam? Multiple-choice questions on Advanced Placement exams have five options: A, B, C, D, and E. A random sample of the correct choice on 400 multiple-choice questions on a variety of AP exams1 shows that B was the most common correct choice, with 90 of the 400 questions having B as the answer. Does this provide evidence that B is more likely to be the correct choice than would be expected if all five options were equally likely? Show all details of the test. The data are available in APMultipleChoice. Click here for the dataset associated with this question. 1http://apcentral.collegeboard.com. Clearly state the null and alternative hypotheses. LINK TO TEXT Calculate the test statistic and p -value. Round your answer for the test statistic to two decimal places, and your answer for the p -value to three decimal places. test statistic = p -value = LINK TO TEXT Can we conclude that B is more likely to be the correct choice? Yes No LINK TO TEXT Question Attempts: 0 of 4 used SAVE FOR LATER SUBMIT ANSWER

Explanation / Answer

Given that,
possibile chances (x)=90
sample size(n)=400
success rate ( p )= x/n = 0.225
success probability,( po )=0.2
failure probability,( qo) = 0.8
null, Ho:p=0.2  
alternate, H1: p>0.2
level of significance, = 0.05
from standard normal table,right tailed z /2 =1.64
since our test is right-tailed
reject Ho, if zo > 1.64
we use test statistic z proportion = p-po/sqrt(poqo/n)
zo=0.225-0.2/(sqrt(0.16)/400)
zo =1.25
| zo | =1.25
critical value
the value of |z | at los 0.05% is 1.64
we got |zo| =1.25 & | z | =1.64
make decision
hence value of |zo | < | z | and here we do not reject Ho
p-value: right tail - Ha : ( p > 1.25 ) = 0.10565
hence value of p0.05 < 0.10565,here we do not reject Ho
ANSWERS
---------------
null, Ho:p=0.2
alternate, H1: p>0.2
test statistic: 1.25
critical value: 1.64
decision: do not reject Ho
p-value: 0.1056
no we don't have evidence that B is more likely to be the correct
choice than would be expected

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