The samples of extensibility of clothings measured in of hi

The samples of extensibility of clothings (measured in %) of high quality fabric and low quality fabric is listed in column J and K. Conduct a test of hypothesis at a significance level of 0.05 to decide if population average extensibility differs for the two types of fabric. (Be sure to write the null hypothesis, alternative hypothesis and your conclusion)

Solution

Set Up Hypothesis
Null , Ho: u1 = u2
Alternate, - H1: u1 != u2
Test Statistic
X(Mean)=1.5083
Standard Deviation(s.d1)=0.4442 ; Number(n1)=24
Y(Mean)=1.5875
Standard Deviation(s.d2)=0.5303; Number(n2)=8
we use Test Statistic (t) = (X-Y)/Sqrt(s.d1^2/n1)+(s.d2^2/n2)
to =1.5083-1.5875/Sqrt((0.19731/24)+(0.28122/8))
to =-0.38
| to | =0.38
Critical Value
The Value of |t | with Min (n1-1, n2-1) i.e 7 d.f is 2.365
We got |to| = 0.38029 & | t | = 2.365
Make Decision
Hence Value of |to | < | t | and Here we Do not Reject Ho
P-Value: Two Tailed ( double the one tail ) - Ha : ( P != -0.3803 ) = 0.715
Hence Value of P0.05 < 0.715,Here We Do not Reject Ho

Population average is similar to the two fabric