Question

Using traditional methods, it takes 10.5 hours to receive a basic flying license. A new license training method using Computer Aided Instruction (CAI) has been proposed. A researcher used the technique with 10 students and observed that they had a mean of 10.2 hours with a standard deviation of 1.3. A level of significance of 0.1 will be used to determine if the technique performs differently than the traditional method. Assume the population distribution is approximately normal. State the null and alternative hypotheses.

Null and alternative hypotheses

Ho : = 10.5

Ha : 10.5

Level of significance a = 0.10

Test statistic t

t = ( xbar - )/(s/√n)

t = ( 10.2 - 10.5)/(1.3/√10)

t = - 0.73

tCritical for a = 0.10 and d.f = n -1 = 9

tCritical = t​​​​​​a/2 , n -1 = t​​​​​​0.05 , 9

tCritical = -1.83

Here tCritical = -1.83 < -0.73

Decision : we fail to reject the null hypothesis Ho

Conclusion : There is no sufficient evidence to support the claim that the technique performs differently than the traditional method