A report from a credibal source states that 63% of US adult citizens favor more
ID: 3315428 • Letter: A
Question
A report from a credibal source states that 63% of US adult citizens favor more regulated gun control laws. To determine if the citizens in the northeast region of the US differed significantly in some way from this national claim, a random sample of 150 adults from the US northeast was collect. In this sample group, 106 stated a preference for more restrictive gun control laws. Follow the steps below to conduct a hypothesis test to determine, at the 2.5% significance level, if the proportion of adults in the northeast region of the US in favor of more restrictive gun control laws was different from the 63% claim.
Give the null and alternative hypotheses for this situation in mathematical notation.
2. Based upon a 2.5% level of significance, determine the appropriate critical value(s) associated with this hypothesis test.
3. Determine the sample's test statistic.
4. Determine the sample's P-value.
Explanation / Answer
Given that,
possibile chances (x)=106
sample size(n)=150
success rate ( p )= x/n = 0.7067
success probability,( po )=0.63
failure probability,( qo) = 0.37
null, Ho:p=0.63
alternate, H1: p!=0.63
level of significance, = 0.025
from standard normal table, two tailed z /2 =2.24
since our test is two-tailed
reject Ho, if zo < -2.24 OR if zo > 2.24
we use test statistic z proportion = p-po/sqrt(poqo/n)
zo=0.70667-0.63/(sqrt(0.2331)/150)
zo =1.9448
| zo | =1.9448
critical value
the value of |z | at los 0.025% is 2.24
we got |zo| =1.945 & | z | =2.24
make decision
hence value of |zo | < | z | and here we do not reject Ho
p-value: two tailed ( double the one tail ) - Ha : ( p != 1.94483 ) = 0.0518
hence value of p0.025 < 0.0518,here we do not reject Ho
ANSWERS
---------------
null, Ho:p=0.63
alternate, H1: p!=0.63
test statistic: 1.9448
critical value: -2.24 , 2.24
decision: do not reject Ho
p-value: 0.0518
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