B Genetically engineered white blood cells were infused into

(B) Genetically engineered white blood cells were infused into 11 patients having melanoma. The doubling time for these white blood cells infused into these 11 patients in terms of days are as follows:

1.4, 1.0, 1.3, 1.0, 1.3, 2.0, 0.6, 0.8, 0.7, 0.9, 1.3

Using a significance level of 5% does this sample support the claim that the mean doubling time for all melanoma patients infused with genetically engineered white cells is less than 1.3 days.

Solution

Set Up Hypothesis
Null, H0: U=1.3
Alternate,genetically engineered white cells is less than 1.3 days H1: U<1.3
Test Statistic
Population Mean(U)=1.3
Sample X(Mean)=1.118
Standard Deviation(S.D)=0.397
Number (n)=11
we use Test Statistic (t) = x-U/(s.d/Sqrt(n))
to =1.118-1.3/(0.397/Sqrt(10))
to =-1.52
| to | =1.52
Critical Value
The Value of |t | with n-1 = 10 d.f is 1.812
We got |to| =1.52 & | t | =1.812
Make Decision
Hence Value of |to | < | t | and Here we Do not Reject Ho
P-Value :Left Tail -Ha : ( P < -1.5205 ) = 0.07968
Hence Value of P0.05 < 0.07968,Here We Do not Reject Ho

We don\'t have evidence to support genetically engineered white cells is less than 1.3 days