An upper one-tailed z-test is performed at an alpha = 0.02. The sample percentag

Question

An upper one-tailed z-test is performed at an alpha = 0.02. The sample percentage was 20% and the random sample size was 200. You are testing whether the sample percentage is significantly more than the population of 15%. You conclude: _______.

you should accept the alternate hypothesis (is significantly less)

b

there is not enough data

c

the null hypothesis could not be rejected

d

the analysis has been designed incorrectly

you should accept the alternate hypothesis (is significantly less)

b

there is not enough data

c

the null hypothesis could not be rejected

d

the analysis has been designed incorrectly

Explanation / Answer

Given that,
possibile chances (x)=30
sample size(n)=200
success rate ( p )= x/n = 0.15
success probability,( po )=0.2
failure probability,( qo) = 0.8
null, Ho:p=0.2
alternate, H1: p>0.2
level of significance, a = 0.02
from standard normal table,right tailed z a/2 =2.05
since our test is right-tailed
reject Ho, if zo > 2.05
we use test statistic z proportion = p-po/sqrt(poqo/n)
zo=0.15-0.2/(sqrt(0.16)/200)
zo =-1.7678
| zo | =1.7678
critical value
the value of |z a| at los 0.02% is 2.05
we got |zo| =1.768 & | z a | =2.05
make decision
hence value of |zo | < | z a | and here we do not reject Ho
p-value: right tail - Ha : ( p > -1.76777 ) = 0.96145
hence value of p0.02 < 0.96145,here we do not reject Ho

ANSWERS
---------------
null, Ho:p=0.2
alternate, H1: p>0.2
test statistic: -1.7678
critical value: 2.05
decision: do not reject Ho
p-value: 0.96145
c.
the null hypothesis could not be rejected

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