Question

A hospital claims that the proportion, p, of full-term babies born in their hospital that weigh more than 7 pounds is 41%. In a random sample of 145 babies born in this hospital, 65 weighed over 7 pounds. Is there enough evidence to reject the hospital's claim at the 0.01 level of significance? Perform a two-tailed test. Then fill in the table below. Carry your intermediate computations to at least three decimal places and round your answers as specified in the table. μ a H. : р The null hypothesis: S D> The alternative hypothesis: H:0 : D=0 DO DO The type of test statistic: (Choose one) DO D<D D>D The value of the test statistic: (Round to at least three decimal places.) x ? The two critical values at the 0.01 level of significance: (Round to at least three decimal places.) and | Can we reject the claim that the proportion of full- term babies born in their hospital that weigh more O Yes O No than 7 pounds is 41%?

Answer 1

Given that,
possibile chances (x)=65
sample size(n)=145
success rate ( p )= x/n = 0.448
success probability,( po )=0.41
failure probability,( qo) = 0.59
null, Ho:p=0.41
alternate, H1: p>0.41
level of significance, α = 0.01
from standard normal table,right tailed z α/2 =2.326
since our test is right-tailed
reject Ho, if zo > 2.326
we use test statistic z proportion = p-po/sqrt(poqo/n)
zo=0.44828-0.41/(sqrt(0.2419)/145)
zo =0.937
| zo | =0.937
critical value
the value of |z α| at los 0.01% is 2.326
we got |zo| =0.937 & | z α | =2.326
make decision
hence value of |zo | < | z α | and here we do not reject Ho
p-value: right tail - Ha : ( p > 0.93711 ) = 0.17435
hence value of p0.01 < 0.17435,here we do not reject Ho
ANSWERS
---------------
null, Ho:p=0.41
alternate, H1: p>0.41
test statistic: 0.937
critical value: 2.326
decision: do not reject Ho
p-value: 0.17435
we do not have enough evidence to support the claim that proportion of full term babies born in their hospital that weigh more than 7 pounds is 41%