Find standardeedtest statistic Round to two decnal places as needed) e Decide wh

Question

Find standardeedtest statistic Round to two decnal places as needed) e Decide whether to reject or fail to reject the nuil hypothesis Choose the correct answer below O Fal to reject Ho el Inbergret the decsion in the conbext of the original claim Choose the corect answer below A. These is enough evidence to support te dam that more than 38% ofUS households own a dog C. There is not erogheidence to spportthe dam tat less than 38% of ushuseholds own adogD. There is enough evidence to support the chin that less than 38% ofus households onadog There is not enough e idence to support te dam harusofus houseoas a nang OB.

Explanation / Answer

Given that,
possibile chances (x)=38
sample size(n)=100
success rate ( p )= x/n = 0.38
success probability,( po )=0.5
failure probability,( qo) = 0.5
null, Ho:p=0.5  
alternate, H1: p<0.5
level of significance, = 0.05
from standard normal table,left tailed z /2 =1.64
since our test is left-tailed
reject Ho, if zo < -1.64
we use test statistic z proportion = p-po/sqrt(poqo/n)
zo=0.38-0.5/(sqrt(0.25)/100)
zo =-2.4
| zo | =2.4
critical value
the value of |z | at los 0.05% is 1.64
we got |zo| =2.4 & | z | =1.64
make decision
hence value of | zo | > | z | and here we reject Ho
p-value: left tail - Ha : ( p < -2.4 ) = 0.0082
hence value of p0.05 > 0.0082,here we reject Ho
ANSWERS
---------------
null, Ho:p=0.5
alternate, H1: p<0.5
c.
test statistic: -2.4
critical value: -1.64
d.
decision: reject Ho
p-value: 0.0082
e.
we have enough evidence to support the claim that les than 38% of US households own a dog

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