Question

Using traditional methods, it takes 9.4 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 23 students and observed that they had a mean of 9.0 hours with a standard deviation of 1.4. 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. Is there sufficient evidence to support the claim that the technique performs differently than the traditional method?

O There is NOT sufficient evidence to support the claim that the technique performs differently than the traditional method?

O There IS sufficient evidence to support the claim that the technique performs differently than the traditional method?

Please show all steps required to answer this question.

Answer 1

Given that, sample size (n) = 23

sample mean = 9.0 hours and

sample standard deviation (s) = 1.4 hours

The null and alternative hypotheses are,

H0 : μ = 9.4 hours

Ha : μ ≠ 9.4 hours

Test statistic is,

=> Test statistic = t = -1.370

t-critical values at significance level of 0.10 with degrees of freedom = 23 - 1 = 22 are, t^* = ±1.717

Excel Command : =TINV(0.10, 22) = 1.717

=> Critical values = ± 1.717

Since, test statistic = -1.370 > -1.717, we fail to reject the null hypothesis.

Therefore, there is not sufficient evidence to support the claim that the technique performs differently than the traditional method.

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