Consider the following two questions designed to assess quantitative literacy 1,
ID: 3313903 • Letter: C
Question
Consider the following two questions designed to assess quantitative literacy 1, what is 15% of 1000? 2, A store is offering a 15% off sale on all TVs. The most popular television is normally priced at $1000. How much money would a customer save on the television during this sale? Suppose the first question is asked of 200 randomly selected college students, with 169 answering correctly; the second one is asked of a different random sample of 200 college students, resulting in 149 correct responses. Carry out a test of hypotheses at significance level 0.05 to decide if the true proportion of correct responses to the question without context exceeds that for the one with context. (Use p1 for the true proportion students who answered the question without context correctly and p2 for the true proportion of students who answered the question with context correctly.) State the relevant hypotheses. Ho: p1-p2 = 0 Ha: P1 P20 Ho: p1-p2 = 0 Ha: P1-P2 > 0 Ho: Pi - P2Explanation / Answer
Given that,
sample one, x1 =169, n1 =200, p1= x1/n1=0.845
sample two, x2 =149, n2 =200, p2= x2/n2=0.745
null, Ho: p1 - p2 = 0
alternate, H1: p1 - p2 > 0
level of significance, = 0.05
from standard normal table,right tailed z /2 =1.645
since our test is right-tailed
reject Ho, if zo > 1.645
we use test statistic (z) = (p1-p2)/(p^q^(1/n1+1/n2))
zo =(0.845-0.745)/sqrt((0.795*0.205(1/200+1/200))
zo =2.477
| zo | =2.477
critical value
the value of |z | at los 0.05% is 1.645
we got |zo| =2.477 & | z | =1.645
make decision
hence value of | zo | > | z | and here we reject Ho
p-value: right tail - Ha : ( p > 2.4771 ) = 0.00662
hence value of p0.05 > 0.00662,here we reject Ho
ANSWERS
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null, Ho: p1 - p2 = 0
alternate, H1: p1 - p2 > 0
test statistic: 2.48
critical value: 1.645
decision: reject Ho
p-value: 0.00662