Question 3 of 6 , Step 4 of 6
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Using traditional methods it takes 109 hours to receive an advanced flying license. A new training technique using Computer Aided instruction (CAI) has been proposed. A researcher used the technique on 210 students and observed that they had a mean of 110 hours. Assume the population standard deviation is known to be 6 . is there evidence at the 0.05 level that the technique lengthens the training time?

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

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Step 1 ：Given that the population mean (μ) is 109 hours, the population standard deviation (σ) is 6 hours, the sample size (n) is 210 students, and the sample mean (X) is 110 hours.

Step 2 ：We are conducting a one-sample z-test. The test statistic (z) can be calculated using the formula: \(z = \frac{X - μ}{σ/\sqrt{n}}\).

Step 3 ：Substituting the given values into the formula, we get: \(z = \frac{110 - 109}{6/\sqrt{210}}\), which simplifies to \(z = 2.4152294576982394\).

Step 4 ：The P-value is the probability that we would observe a result as extreme as the test statistic, assuming the null hypothesis is true. In this case, the null hypothesis is that the mean training time is 109 hours. We are testing the alternative hypothesis that the mean training time is greater than 109 hours.

Step 5 ：Using the calculated z-score, we find that the P-value is 0.007862649877252714.

Step 6 ：Rounding to four decimal places, the final answer is: \(\boxed{0.0079}\).