Using traditional methods, it takes 98 hours to receive a basic driving license. A new license training method using Computer Aided Instruction (CAI) has been proposed. A researcher used the technique with 270 students and observed that they had a mean of 97 hours. Assume the standard deviation is known to be 7. A level of significance of 0.1 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?

Step-by-step explanation:

We would set up the hypothesis test.

For the null hypothesis,

µ = 98

For the alternative hypothesis,

µ ≠ 98

This is a 2 tailed test.

Since no population standard deviation is given, the distribution is a student's t.

Since n = 270

Degrees of freedom, df = n - 1 = 270 - 1 = 269

t = (x - µ)/(s/√n)

Where

x = sample mean = 97

µ = population mean = 98

s = samples standard deviation = 7

t = (97 - 98)/(7/√270) = - 2.35

We would determine the p value using the t test calculator. It becomes

p = 0.02

Since alpha, 0.1 > than the p value, 0.02, then we would reject the null hypothesis. Therefore, At a 10% level of significance, there sufficient evidence to support the claim that the technique performs differently than the traditional method.