In Exercises 5–16, use analysis of variance for the indicated ...

Question

In Exercises 5–16, use analysis of variance for the indicated test.

Triathlon Times Jeff Parent is a statistics instructor who participates in triathlons. Listed below are times (in minutes and seconds) he recorded while riding a bicycle for five stages through each mile of a 3-mile loop. Use a 0.05 significance level to test the claim that it takes the same time to ride each of the miles. Does one of the miles appear to have a hill?

Triathlon bike times table: Mile 1 (3:15-3:24), Mile 2 (3:17-3:22), Mile 3 (3:29-3:34).

Accepted Answer

Hello. In this video, we are told that a hiking trail passes through 3 different zones of a forest. A researcher measures the elevation gain for 5 separate hikes in each zone. The recorded elevation gains are shown below in the table. We want to use a 0.05 significance level to test the claim that the mean elevation gain is the same for all three zones, and based on the results, doesn't appear that any zone includes a steep incline. So, in order to approach this problem, let's go ahead and set up a hypothesis. Now, we want to test the claim that the mean elevation gains are the same for all three zones. So, our null hypothesis is stating that the mean elevation gain for zone A, zone B, and zone C are all going to be the same. And our alternate hypothesis is stating the opposite, where at least one. Is different So, let's go ahead and calculate the mean elevation gains for each zone. For zone A, we are going to take the sum of all the measurements, so 110 plus 108 plus 112, plus 109, plus 111, and we are going to divide this by the total amount of data points that we are adding, which is 5. This is going to give us a mean elevation gain of 110. We are then going to repeat this process for zone B. We have 95 plus 92 + 94 + 93 + 96 divided by 5, and we get a mean elevation gain of 94.0. And finally for zone C. We have 132 plus 129 plus 134. Plus 131 + 133, divided by 5, and that gives us a mean elevation gain of 131.3. Now, what we are going to do is we are going to perform a one direction Enova test. Now, in order to do this Enova test, we will need to use a calculator or a software, but by performing the Enova test, we will get an F statistic of 620.71, and we get a P value. That is less than 0.0001. Now, recall that we are working with a 0.05 significance level. If we compare this P-value to the significance level, the P-value is less than the significance level, and that means that we're going to reject our null hypothesis. Now, since we are rejecting our no hypothesis, that tells us that at least one of the elevation means are going to be different compared to the others. And in order to identify this mean, we are just going to compare the means we calculated earlier. Notice that from amongst the three means, zone C has the highest elevation with a mean of 131.3. So what that means is that zone C has the highest elevation, and the solution to this problem is going to be D. So I hope this video helps you in understanding how to approach this problem, and we will go ahead and see you all in the next video.

Key Concepts

Analysis of Variance (ANOVA)

Significance Level

Null and Alternative Hypotheses

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