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Researchers in Yellowstone National Park are studying the Old Faithful geyser. They want to use the length of each eruption to predict the amount of time that will elapse before the next eruption. In particular, they believe that when the geyser erupts for a longer period of time, the amount of time before the next eruption will also be longer. Below are the lengths of 16 randomly chosen eruptions along with the amount of time until the next eruption. The two data sets are in the same order and are both measured in minutes. Eruption length: 3.9, 4.3, 2.2, 3.7, 4, 1.9, 5.3, 4.3, 4.5, 1.9, 4.5, 2.2, 2.1, 4, 1.8, 3.3 Time to next eruption: 69, 87, 60, 71, 108, 50, 77, 89, 84, 60, 80, 60, 49, 92, 43, 74 Conduct a hypothesis test to determine whether there is evidence that when the geyser erupts for a longer period of time, the amount of time before the next eruption will also be longer. Step 1: State hypotheses. Step 2: Verify whether the conditions are met for the hypothesis test (even if one of the conditions is not met, continue with the rest of the hypothesis test). Step 3: Report the P-value of the test. Step 4: State the conclusion using a significance level of α = 0.05, both in statistical terms and in the context of the problem.

          Researchers in Yellowstone National Park are studying the Old Faithful geyser. They want to use the length of each eruption to predict the amount of time that will elapse before the next eruption. In particular, they believe that when the geyser erupts for a longer period of time, the amount of time before the next eruption will also be longer. Below are the lengths of 16 randomly chosen eruptions along with the amount of time until the next eruption. The two data sets are in the same order and are both measured in minutes.

Eruption length: 3.9, 4.3, 2.2, 3.7, 4, 1.9, 5.3, 4.3, 4.5, 1.9, 4.5, 2.2, 2.1, 4, 1.8, 3.3
Time to next eruption: 69, 87, 60, 71, 108, 50, 77, 89, 84, 60, 80, 60, 49, 92, 43, 74

Conduct a hypothesis test to determine whether there is evidence that when the geyser erupts for a longer period of time, the amount of time before the next eruption will also be longer.

Step 1: State hypotheses.
Step 2: Verify whether the conditions are met for the hypothesis test (even if one of the conditions is not met, continue with the rest of the hypothesis test).
Step 3: Report the P-value of the test.
Step 4: State the conclusion using a significance level of α = 0.05, both in statistical terms and in the context of the problem.

Added by Jacqueline N.

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