Please and thank you An article in a journal reports that 74% of American father

Question

Please and thank you An article in a journal reports that 74% of American fathers take responsibility for child care. A researcher claims that the figure is lower for fathers in the town of Littleton. A random sample of 234 fathers from Littleton yield 150 who helped with child care. Test the researcher's claim at the 0.05 significance level. Express the original claim in symbolic form. Identify the conclusion about the null hypothesis (reject or fall to reject Ho). Give a reason for your answer. Write the final conclusion that addresses the original claim.

Explanation / Answer

a)
Research cliam that lower than 74% of american father take responsibiity for child care in town littleton
b)
Set Up Hypothesis
Null, H0:P=0.74
Alternate, H1: P<0.74
c)
Critical Value
The Value of |Z | at LOS 0.05% is, When Zo<-1.64, Reject Ho
Test Statistic
No. Of Success chances Observed (x)=150
Number of objects in a sample provided(n)=234
No. Of Success Rate ( P )= x/n = 0.641
Success Probability ( Po )=0.74
Failure Probability ( Qo) = 0.26
we use Test Statistic (Z) for Single Proportion = P-Po/Sqrt(PoQo/n)
Zo=0.64103-0.74/(Sqrt(0.1924)/234)
Zo =-3.4517
| Zo | =3.4517
We got |Zo| =3.452 & | Z | =1.64
d)
Make Decision
Hence Value of | Zo | > | Z | and Here we Reject Ho
P-Value: Left Tail -Ha : ( P < -3.45166 ) = 0.00028
Hence Value of P0.05 > 0.00028,Here we Reject Ho

We have evidence to support the fighure is lower for fathers in the town of littleton

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