a local charity thinks that people in river heights give mor

a local charity thinks that people in river heights give more money to their charity than people in lake view. they conducted a survey of 25 people in each subdivision and recorded the results. is their hypothesis correct. let alpha equals .01 X1=$30, X2=$20, S1=$3, S2=$4, N1=25, N2=25

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)=30
Standard Deviation(s.d1)=3 ; Number(n1)=25
Y(Mean)=20
Standard Deviation(s.d2)=4; Number(n2)=25
we use Test Statistic (t) = (X-Y)/Sqrt(s.d1^2/n1)+(s.d2^2/n2)
to =30-20/Sqrt((9/25)+(16/25))
to =10
| to | =10
Critical Value
The Value of |t | with Min (n1-1, n2-1) i.e 24 d.f is 1.711
We got |to| = 10 & | t | = 1.711
Make Decision
Hence Value of | to | > | t | and Here we Reject Ho
P-Value:Right Tail -Ha : ( P > 10 ) = 0
Hence Value of P0.05 > 0,Here we Reject Ho