A phone manufacturer wants to compete in the touch screen ph

A phone manufacturer wants to compete in the touch screen phone market. He understands that the lead product has a battery life of just 4 hours. The manufacturer claims that while the new touch phone is more expensive, its battery life is more than twice as long as that of the leading product. In order to test the claim, a researcher samples 45 units of the new phone and finds that the sample battery life averages 9.0 hours with a sample standard deviation of 2.5 hours. Null and alternative hypothesis of H₀: 8; H_A: > 8

A)Compute the value of the appropriate test statistic

B) Calculate the critical value to test the phone manufacturer\'s claim at a= 0.10

Solution

Set Up Hypothesis
Null, H0: U<=8
Alternate, H1: U>8
Test Statistic
Population Mean(U)=8
Sample X(Mean)=9
Standard Deviation(S.D)=2.5
Number (n)=45
we use Test Statistic (t) = x-U/(s.d/Sqrt(n))
to =9-8/(2.5/Sqrt(44))
to =2.683
| to | =2.683
Critical Value
The Value of |t | with n-1 = 44 d.f is 1.301
We got |to| =2.683 & | t | =1.301
Make Decision
Hence Value of | to | > | t | and Here we Reject Ho
P-Value :Right Tail - Ha : ( P > 2.6833 ) = 0.00512
Hence Value of P0.1 > 0.00512,Here we Reject Ho