Consider the following hypothesis test. H 0 : 1 - 2 0 H a : 1 - 2 > 0 The follow

Question

Consider the following hypothesis test.

H0: 1 - 2 0
Ha: 1 - 2 > 0

The following results are for two independent samples taken from the two populations.

a. What is the value of the test statistic (round to 2 decimals)?

b. What is the p-value (round to 4 decimals)? Use z-value rounded to 2 decimal places.

c. With = .05, what is your hypothesis testing conclusion?

p-value is ____________ H0 :

greater than or equal to 0.05, reject

greater than 0.05, do not reject

less than or equal to 0.05, reject

less than 0.05, do not rejectequal to 0.05, reject

not equal to 0.05, reject

Explanation / Answer

Set Up Hypothesis
Null, Ho: u1 - u2 <=0
Alternate, H1: u1 - u2 > 0
Test Statistic
X(Mean)=25.3
Standard Deviation(s.d1)=5.7
Number(n1)=30
Y(Mean)=22.7
Standard Deviation(s.d2)=7
Number(n2)=60
we use Test Statistic (Z) = (X-Y)/Sqrt(s.d1^2/n1)+(s.d2^2/n2)
Zo=25.3-22.7/Sqrt((32.49/30)+(49/60))
Zo =1.89
| Zo | =1.89
Critical Value
The Value of |Z | at LOS 0.05% is 1.645
We got |Zo | =1.886 & | Z | =1.645
Make Decision
Hence Value of | Zo | > | Z | and Here we Reject Ho
P-Value: Right Tail -Ha : ( P > 1.89 ) = 0.02962
Hence Value of P0.05 > 0.02962,Here we Reject Ho

[ANSSWERS]
a. Zo =1.89
b. P-Value: Right Tail -Ha : ( P > 1.89 ) = 0.02962
c. p-value is ____________ H0, less than or equal to 0.05, reject

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