Predicting Old Faithful: The Old Faithful geyser in Yellowstone National Park in Wyoming has its name because of its regularly spaced eruptions. The time between eruptions is usually about 1.5 hours, but periodically, this time is closer to 1 hour. Immediately after each eruption, National Park Service personnel make an effort to predict the time until the next one in order to allow park visitors to be present when it occurs without having to wait the entire time period between eruptions. The data file ‘OLD FAITHFUL.xlsx’ has data for a random selection of 40 prediction errors (in minutes). Negative prediction errors indicate the geyser erupted prior to the predicted time, positive values indicate the number of minutes past the predicted time when the geyser actually erupted. Use the available data to assess the accuracy of the National Park Service predictions at the 10% level of significance. a. What is the inherent question of interest here? b. What might be a reasonable description of the population of interest? c. What is the relevant sample here? d. What is the random variable being evaluated here? e. What is the population parameter of interest? f. What is this parameter’s corresponding sample statistic? g. What is an appropriate research hypothesis to consider? h. What is the corresponding null hypothesis? i. What is the test statistic used to test these hypotheses? j. What is the null distribution of this test statistic? k. What is the decision rule that might be used here (use α = 0.10)?
- Predicting Old Faithful: The Old Faithful geyser in Yellowstone National Park in Wyoming has its name because of its regularly spaced eruptions. The time between eruptions is usually about 1.5 hours, but periodically, this time is closer to 1 hour. Immediately after each eruption, National Park Service personnel make an effort to predict the time until the next one in order to allow park visitors to be present when it occurs without having to wait the entire time period between eruptions. The data file ‘OLD FAITHFUL.xlsx’ has data for a random selection of 40 prediction errors (in minutes). Negative prediction errors indicate the geyser erupted prior to the predicted time, positive values indicate the number of minutes past the predicted time when the geyser actually erupted. Use the available data to assess the accuracy of the National Park Service predictions at the 10% level of significance.
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a. What is the inherent question of interest here? |
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b. What might be a reasonable description of the population of interest? |
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c. What is the relevant sample here? |
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d. What is the random variable being evaluated here? |
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e. What is the population parameter of interest? |
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f. What is this parameter’s corresponding sample statistic? |
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g. What is an appropriate research hypothesis to consider? |
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h. What is the corresponding null hypothesis? |
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i. What is the test statistic used to test these hypotheses? |
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j. What is the null distribution of this test statistic? |
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k. What is the decision rule that might be used here (use α = 0.10)? |
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l. What decision was made with regard to the null hypothesis? |
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m. What is your conclusion based on the available data? |
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n. What is your best point estimate of the average error for the National Park Service’s predictions? |
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o. Provide a 90% confidence interval for the average prediction error for the National Park Service’s estimated eruption times.
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p. Given the results of your evaluation, do you consider the National Park Service predictions of Old Faithful eruption times to be accurate? If so, why? If not, why not? |
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