A sample of students attending a large university has been s

A sample of students attending a large university has been selected. Is there a statistically significant difference between Liberal Arts majors and other students on average number of books (other than those required by course work) read per year? Use the five step model and write a sentence or two interpreting your results.

Liberal Arts               Other

X₁= 16.2                    X₂ = 13.7

s₁ =   2.3                      s₂ = 9.0

N₁ = 236                     N₂ = 321

Solution

Set Up Hypothesis
Null, no difference between Liberal Arts majors and other students Ho: u1 = u2
Alternate, significant difference between Liberal Arts majors and other students H1: u1 != u2
Test Statistic
X(Mean)=16.2
Standard Deviation(s.d1)=2.3
Number(n1)=236
Y(Mean)=13.7
Standard Deviation(s.d2)=9
Number(n2)=321
we use Test Statistic (Z) = (X-Y)/Sqrt(s.d1^2/n1)+(s.d2^2/n2)
Zo=16.2-13.7/Sqrt((5.29/236)+(81/321))
Zo =4.77
| Zo | =4.77
Critical Value
The Value of |Z | at LOS 0.05% is 1.96
We got |Zo | =4.769 & | Z | =1.96
Make Decision
Hence Value of | Zo | > | Z | and Here we Reject Ho
P-Value: Two Tailed ( double the one tail ) - Ha : ( P != 4.77 ) = 0
Hence Value of P0.05 > 0,Here we Reject Ho

At 95%, 90% , 99% Level of confidence we have evidence to support that it has significant difference between Liberal Arts majors and other students