The resting heart rates were measured in a sample of women s

The resting heart rates were measured in a sample of women smokers and non smokers at a state university. There were 14 smokers and 18 non smokers in the sample. Was there a significant difference in the resting heart rates of the two groups? Use alpha .05. (Use a two-tailed test.)

Resting Heart Rates

78, 100, 88, 62, 94, 88, 76, 90, 85, 82, 77, 91, 90, 68

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)=83.5
Standard Deviation(s.d1)=10.376 ; Number(n1)=14
Y(Mean)=72.5
Standard Deviation(s.d2)=10.331; Number(n2)=18
we use Test Statistic (t) = (X-Y)/Sqrt(s.d1^2/n1)+(s.d2^2/n2)
to =83.5-72.5/Sqrt((107.66138/14)+(106.72956/18))
to =2.98
| to | =2.98
Critical Value
The Value of |t | with Min (n1-1, n2-1) i.e 13 d.f is 2.16
We got |to| = 2.98066 & | t | = 2.16
Make Decision
Hence Value of | to | > | t | and Here we Reject Ho
P-Value: Two Tailed ( double the one tail ) - Ha : ( P != 2.9807 ) = 0.011
Hence Value of P0.05 > 0.011,Here we Reject Ho

We have evidence that significant difference in the resting heart rates of the two groups