An organization wants to have some merchandise produced that will promote its ca

Question

An organization wants to have some merchandise produced that will promote its cause at an upcoming event. From previous experience, the organization believes that that 35% of event patrons will purchase the merchandise. A promoter for the organization claims that this percentage is not accurate. At a recent event, 60 randomly selected patrons were surveyed, and 18 of those patrons indicated that they would purchase the merchandise. With 90% confidence, is there sufficient evidence to suggest that the percentage of patrons who would purchase the merchandise is different than 35%? Use the step-by-step process for hypothesis testing. Include the process of determining the test statistic and corresponding p-value as part of your hypothesis test. (If an approximate p-value cannot be determined from the Z cumulative probability table, use bracketing in the t probability able to estimate the p-value range.)

Explanation / Answer

Given that,
possibile chances (x)=18
sample size(n)=60
success rate ( p )= x/n = 0.3
success probability,( po )=0.35
failure probability,( qo) = 0.65
null, Ho:p=0.35
alternate, H1: p!=0.35
level of significance, = 0.1
from standard normal table, two tailed z /2 =1.64
since our test is two-tailed
reject Ho, if zo < -1.64 OR if zo > 1.64
we use test statistic z proportion = p-po/sqrt(poqo/n)
zo=0.3-0.35/(sqrt(0.2275)/60)
zo =-0.812
| zo | =0.812
critical value
the value of |z | at los 0.1% is 1.64
we got |zo| =0.812 & | z | =1.64
make decision
hence value of |zo | < | z | and here we do not reject Ho
p-value: two tailed ( double the one tail ) - Ha : ( p != -0.812 ) = 0.41679
hence value of p0.1 < 0.4168,here we do not reject Ho

ANSWERS
---------------
null, Ho:p=0.35
alternate, H1: p!=0.35
test statistic: -0.812
critical value: -1.64 , 1.64
decision: do not reject Ho
p-value: 0.41679

we don't have evidence to support sample is diffrent from 35%

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