A recent survey compared the costs of adoption through publi

A recent survey compared the costs of adoption through public and private agencies. For a sample of 16 adoptions through a public agency, the mean cost was $21,045, with a standard deviation of $835. For a sample of 18 adoptions through a private agency, the mean cost was $22,840, with a standard deviation of $1,545. Can we conclude the mean cost is larger for adopting children through a private agency? Use the .05 significance level. Find the degrees of freedom for unequal variance test. (Round down your answer to the nearest whole number.) State the decision rule for .05 significance level: H0: mu c GE mu r ; H1 : mu c smallerthan mu r. (Negative amount should be indicated by a minus sign. Round your answer to 3 decimal places.) Compute the value of the test statistic. (Negative amount should be indicated by a minus sign. Round your answer to 3 decimal places.) Can we conclude the mean cost is larger for adopting children from a private agency? Use the 0.05 significance level.

Solution

Set Up Hypothesis
Null Hypothesis , There Is No-Significance between them Ho: u1 > u2
Alternate Hypothesis, There Is Significance between them - H1: u1 < u2
Test Statistic
X(Mean)=21045
Standard Deviation(s.d1)=835 ; Number(n1)=16
Y(Mean)=22840
Standard Deviation(s.d2)=1545; Number(n2)=18
we use Test Statistic (t) = (X-Y)/Sqrt(s.d1^2/n1)+(s.d2^2/n2)
to =21045-22840/Sqrt((697225/16)+(2387025/18))
to =-4.276
| to | =4.276
Critical Value
The Value of |t | with Min (n1-1, n2-1) i.e 15 d.f is 1.753
We got |to| = 4.27637 & | t | = 1.753
Make Decision
Hence Value of | to | > | t | and Here we Reject Ho
P-Value:Left Tail - Ha : ( P < -4.2764 ) = 0.00033
Hence Value of P0.05 > 0.00033,Here we Reject Ho

1)Min (n1-1, n2-1) i.e 15 d.f is 1.753
2) Reject Ho, if Z < -1.753
3) to =-4.276
4) Reject Ho, can conclude