Northeastern university (NU) wants to determine if it’s students spend more time

Question

Northeastern university (NU) wants to determine if it’s students spend more time exercising while at college than when at high school (HS). A random sample of 9 NU students was taken. The sample reveals the following data: Daily hours exercising at HS 0 1 1 2 1 1 4 2 1 Daily hours exercising at NU 1 3 5 3 1 1 3 3 2 At the .05 level of significance, is there evidence a student spends more time exercising on average at NU than when at HS? ( Assume the population of differences follows a normal distribution.)

Explanation / Answer

Set Up Hypothesis
Null Hypothesis , There Is No-Significance between them Ho: u1 = u2
Alternate , students spend more time at college than when at high school - H1: u1 < u2
Test Statistic
X(Mean)=1.4444
Standard Deviation(s.d1)=1.1304 ; Number(n1)=9
Y(Mean)=2.4444
Standard Deviation(s.d2)=1.3333; Number(n2)=9
we use Test Statistic (t) = (X-Y)/Sqrt(s.d1^2/n1)+(s.d2^2/n2)
to =1.4444-2.4444/Sqrt((1.2778/9)+(1.77769/9))
to =-1.716
| to | =1.716
Critical Value
The Value of |t | with Min (n1-1, n2-1) i.e 8 d.f is 1.86
We got |to| = 1.71625 & | t | = 1.86
Make Decision
Hence Value of |to | < | t | and Here we Do not Reject Ho
P-Value:Left Tail - Ha : ( P < -1.7163 ) = 0.06223
Hence Value of P0.05 < 0.06223,Here We Do not Reject Ho

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