25 It is claimed that a certain type of bipolar transistor h

25. It is claimed that a certain type of bipolar transistor has a mean value of current gain that is at least 210. A sample of these transistors is tested. If the sample mean value of current gain is 200 with a sample standard deviation of 35, would the claim be rejected at the 5 percent level of significance if (a) the sample size is 25;

Solution

a)
t-test For Single Mean
Set Up Hypothesis
Null Hypothesis H0: U>210
Alternate Hypothesis H1: U<210
Test Statistic
Population Mean(U)=210
Sample X(Mean)=200
Standard Deviation(S.D)=35
Number (n)=25
we use Test Statistic (t) = x-U/(s.d/Sqrt(n))
to =200-210/(35/Sqrt(24))
to =-1.429
| to | =1.429
Critical Value
The Value of |t ?| with n-1 = 24 d.f is 1.71
We got |to| =1.429 & | t ? | =1.71
Make Decision
Hence Value of |to | < | t ? | and Here we Do not Reject Ho
P-Value :Left Tail -Ha : ( P < -1.4286 ) = 0.08301
Hence Value of P0.05 < 0.08301,Here We Do not Reject Ho

b)
Number (n)=64
we use Test Statistic (t) = x-U/(s.d/Sqrt(n))
to =200-210/(35/Sqrt(63))
to =-2.286
| to | =2.286
Critical Value
The Value of |t ?| with n-1 = 63 d.f is 1.67
We got |to| =2.286 & | t ? | =1.67
Make Decision
Hence Value of | to | > | t ?| and Here we Reject Ho
P-Value :Left Tail -Ha : ( P < -2.2857 ) = 0.01282
Hence Value of P0.05 > 0.01282,Here we Reject Ho