Solve the above and find the p-value. Also is there sufficient evidence or not?

Question

Solve the above and find the p-value.

Also is there sufficient evidence or not?

because the p-value is greater than the level of significance. Therefore you do or do not reject the null hypothesis.?

Previously, 42% of parents of children in high school felt it was a serious problem that high school students were not being taught enough math and science. A recent survey found that 120 of 250 parents of children in high school felt it was a serious problem that high school students were not being taught enough math and science. Do parents feel differently today? Use the = 0.1 level of significance. What are the null and alternative hypotheses? versus H1 : p|

Explanation / Answer

Given that,
possible chances (x)=120
sample size(n)=250
success rate ( p )= x/n = 0.48
success probability,( po )=0.42
failure probability,( qo) = 0.58
null, Ho:p=0.42  
alternate, H1: p!=0.42
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=0.48-0.42/(sqrt(0.2436)/250)
zo =1.9221
| zo | =1.9221
critical value
the value of |z | at los 0.1% is 1.64
we got |zo| =1.922 & | z | =1.64
make decision
hence value of | zo | > | z | and here we reject Ho
p-value: two tailed ( double the one tail ) - Ha : ( p != 1.92213 ) = 0.05459
hence value of p0.1 > 0.0546,here we reject Ho
ANSWERS
---------------
null, Ho:p=0.42
alternate, H1: p!=0.42
test statistic: 1.9221
critical value: -1.64 , 1.64
decision: reject Ho
p-value: 0.05459

p-value is less than the level of significance

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