Question

Using traditional methods it takes 105 hours to receive an advanced driving license. A new training technique using Computer Aided Instruction (CAI) has been proposed. A researcher used the technique on 150 students and observed that they had a mean of 104 hours. Assume the population standard deviation is known to be 5. Is there evidence at the 0.05 level that the technique performs differently than the traditional method?

Step 1 of 6: State the null and alternative hypotheses.

Step 2 of 6: Find the value of the test statistic. Round your answer to two decimal places.

Step 3 of 6: Specify if the test is one-tailed or two-tailed.

Step 4 of 6: Find the P-value of the test statistic. Round your answer to four decimal places.

Step 5 of 6: Identify the level of significance for the hypothesis test.

Step 6 of 6: Make the decision to reject or fail to reject the null hypothesis.

Answer 1

Given that, sample size (n) = 150, sample mean = 104 hours

and population standard deviation = 5 hours

Step 1) The null and alternative hypotheses are,

H0 : μ = 105 hours

Ha : μ ≠ 105 hours

Step 2) Test statistic is,

=> Test statistic = Z = -2.45

Step 3) This hypothesis test is a two-tailed test.

Step 4) p-value = 2 * P(Z < -2.45) = 2 * 0.0071 = 0.0142

=> p-value = 0.0142

Step 5) level of significance for the hypothesis test is 0.05

Step 6) Since, p-value is less than significance level of 0.05, we reject the null hypothesis.