Are people waiting longer to marry? In 2007, a random sample of young adults (ag
ID: 3224265 • Letter: A
Question
Are people waiting longer to marry? In 2007, a random sample of young adults (ages 18-31) showed that 468 of 1872 of those surveyed were married. In 2012, 581 of the 1940 young adults (ages 18-31) randomly surveyed were married. Is there any evidence to suggest the true proportion of young adults who are married has decreased? Use = 0.10.
State the name of the hypothesis test that you will be running.
Define the parameter(s).
State the null and alternative hypotheses.
List and check your assumptions.
State the significance level.
Report the value of the test statistic (to three decimal places) and degrees of freedom, if appropriate.
Report the p-value, to four decimal places.
State the result of your test.
State your conclusion in the context of the problem.
Construct and interpret a confidence interval. Explain how the results of the interval are consistent with the result of the hypothesis test.
Explanation / Answer
Given that,
sample one, x1 =468, n1 =1872, p1= x1/n1=0.25
sample two, x2 =581, n2 =1940, p2= x2/n2=0.299
null, Ho: p1 = p2
alternate, H1: p1 < p2
level of significance, a = 0.1
from standard normal table,left tailed z a/2 =
since our test is left-tailed
reject Ho, if zo < -1.282
we use test statistic (z) = (p1-p2)/v(p^q^(1/n1+1/n2))
zo =(0.25-0.299)/sqrt((0.275*0.725(1/1872+1/1940))
zo =-3.42
| zo | =3.42
critical value
the value of |z a| at los 0.1% is 1.282
we got |zo| =3.42 & | z a | =1.282
make decision
hence value of | zo | > | z a| and here we reject Ho
p-value: left tail - Ha : ( p < -3.42 ) = 0.00031
hence value of p0.1 > 0.00031,here we reject Ho
ANSWERS
---------------
null, Ho: p1 = p2
alternate, H1: p1 < p2
test statistic: -3.42
critical value: -1.282
decision: reject Ho
p-value: 0.00031
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