Question

Example: The proportion of households in KSA who prefer shopping in HyperPanda is being studied. From a sample of size 100 households, 70 prefer to shop from HyperPanda. a. Using the critical value approach, can you conclude that less than 75% of households prefer shopping from HyperPanda? b. Do the test again using the p-value approach.

Answer 1

Given that,
possible chances (x)=70
sample size(n)=100
success rate ( p )= x/n = 0.7
success probability,( po )=0.75
failure probability,( qo) = 0.25
null, Ho:p=0.75
alternate, H1: p<0.75
level of significance, α = 0.05
from standard normal table,left tailed z α/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=0.7-0.75/(sqrt(0.1875)/100)
zo =-1.1547
| zo | =1.1547
critical value
the value of |z α| at los 0.05% is 1.64
we got |zo| =1.155 & | z α | =1.64
make decision
hence value of |zo | < | z α | and here we do not reject Ho
p-value: left tail - Ha : ( p < -1.1547 ) = 0.12411
hence value of p0.05 < 0.12411,here we do not reject Ho
ANSWERS
---------------
a.
null, Ho:p=0.75
alternate, H1: p<0.75
test statistic: -1.1547
critical value: -1.64
decision: do not reject Ho
b.
p-value: 0.12411
we do not have enough evidence to support the claim that less than 75%of households prefer
shopping from hyperpanda.