A multiple choice test has four possible responses. To test whether this questio

Question

A multiple choice test has four possible responses. To test whether this question was answered correctly by more people than would be expected due to chance, a hypothesis test of 400 student answers is conducted. a.What is the null and alternative hypothesis (in words and symbols). b. If 218 of the 400 students got the correct response, what is the p-value? Explain your method and TI commands. c. What decision is made if a significance level of 0.01 is used? d. Based on this decision, what would you conclude about the test question?

Explanation / Answer

Given that,
possibile chances (x)=218
sample size(n)=400
success rate ( p )= x/n = 0.545
success probability,( po )=0.25
failure probability,( qo) = 0.75
null, Ho:p=0.25  
alternate, H1: p!=0.25
level of significance, = 0.01
from standard normal table, two tailed z /2 =2.58
since our test is two-tailed
reject Ho, if zo < -2.58 OR if zo > 2.58
we use test statistic z proportion = p-po/sqrt(poqo/n)
zo=0.545-0.25/(sqrt(0.1875)/400)
zo =13.6255
| zo | =13.6255
critical value
the value of |z | at los 0.01% is 2.58
we got |zo| =13.625 & | z | =2.58
make decision
hence value of | zo | > | z | and here we reject Ho
p-value: two tailed ( double the one tail ) - Ha : ( p != 13.62547 ) = 0
hence value of p0.01 > 0,here we reject Ho
ANSWERS
---------------
null, Ho:p=0.25
alternate, H1: p!=0.25
test statistic: 13.6255
critical value: -2.58 , 2.58
decision: reject Ho
p-value: 0
we have enough evidence to support the claim

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