Question

Using traditional methods, it takes 103 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 120 students and observed that they had a mean of 104 hours. Assume the variance is known to be 25. A level of significance of 0.05 will be used to determine if the technique performs differently than the traditional method. Is there sufficient evidence to support the claim that the technique performs differently than the traditional method?

What is the conclusion?

A. There is not sufficient evidence to support the claim that the technique performs differently than the traditional method

OR

B. There is sufficient evidence to support the claim that the technique performs differently than the traditional method.

Answer 1

1) Hypothesis-

H0: = 103

Ha: 103 (Two tailed)

2) Critical region -

Criticla value at 0.05 significance level = -1.96 , 1.96

Critical region is reject H0 if test statistics < -1.96 or test statistics > 1.96

3) Test statistics

z = - / ( / sqrt(n) )

= 104 - 103 / (5 / sqrt(120) )

= 2.19

4) Decision-

Since test statistics value falls in rejection region, we have sufficient evidence to reject H0.

5) p-value

p-value = 2 * P(Z > z) (Where 2 is multiplied to probability since this is two tailed test)

= 2 * P( Z > 2.19)

= 2 * ( 1 - P( Z < 2.19) )

= 2 * ( 1 - 0.98565 )

= 0.0285

6) Conclusion -

There is sufficient evidence to support the claim that the technique performs differently than the

traditional method.