Answer k through p please 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? The inherent question here is to test the accracy of the predictions on time period between eruptions, made by the National Park service personal. b. What might be a reasonable description of the population of interest? The population of interest is the error in the predicted time period between eruptions in the old faithful geyser in Yellowstone National Park in Wyoming. c. What is the relevant sample here? The sample here is the randomly selected 40 prediction error (in minutes). d. What is the random variable being evaluated here? The random variable of interest, here would be "Prediction Error". e. What is the population parameter of interest? the approximate measure to represent the variable would be "Mean". Hence the population parameter here, would be Mean Prediction Error. f. What is this parameter’s corresponding sample statistic? The parameter's corresponding sample statistic would be Sample Mean Prediction Error x. We must note that the sample mean is an unbiased estimator of the population mean. g. What is an appropriate research hypothesis to consider? We may claim the predictions, made by the National Park service personnel to be accurate is the prediction error is equal to Zero. Hence, we may frame the hypothesis as : H0 : μ = 0H0 : μ = 0 Vs H1 : μ ≠ 0H1 : μ ≠ 0 Hence, the research hypothesis would be H1 : μ ≠ 0 h. What is the corresponding null hypothesis? The null hypothesis would be the negation of the research hypothesis : Here, the actual claim to be tested i.e., H0 : μ = 0 i. What is the test statistic used to test these hypotheses? The approximate statistical test to compare the population mean to a hypothesized value (zero), when the population standard deviation is unknown would be "One Sample Test" j. What is the null distribution of this test statistic? The test statistic for the t test would be given by giving 1.73 k. What is the decision rule that might be used here (use α = 0.10)? l. What decision was made with regard to the null hypothesis? m. What is your conclusion based on the available data? n. What is your best point estimate of the average error for the National Park Service’s predictions? o. Provide a 90% confidence interval for the average prediction error for the National Park Service’s estimated eruption times. p. Given the results of your evaluation, do you consider the National Park Service pr
Answer k through p please
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?
The inherent question here is to test the accracy of the predictions on time period between eruptions, made by the National Park service personal.
b. What might be a reasonable description of the population of interest?
The population of interest is the error in the predicted time period between eruptions in the old faithful geyser in Yellowstone National Park in Wyoming.
c. What is the relevant sample here?
The sample here is the randomly selected 40 prediction error (in minutes).
d. What is the random variable being evaluated here?
The random variable of interest, here would be "Prediction Error".
e. What is the population parameter of interest?
the approximate measure to represent the variable would be "Mean". Hence the population parameter here, would be Mean Prediction Error.
f. What is this parameter’s corresponding sample statistic?
The parameter's corresponding sample statistic would be Sample Mean Prediction Error x. We must note that the sample mean is an unbiased estimator of the population mean.
g. What is an appropriate research hypothesis to consider?
We may claim the predictions, made by the National Park service personnel to be accurate is the prediction error is equal to Zero. Hence, we may frame the hypothesis as :
H0 : μ = 0H0 : μ = 0 Vs H1 : μ ≠ 0H1 : μ ≠ 0
Hence, the research hypothesis would be H1 : μ ≠ 0
h. What is the corresponding null hypothesis?
The null hypothesis would be the negation of the research hypothesis :
Here, the actual claim to be tested i.e.,
H0 : μ = 0
i. What is the test statistic used to test these hypotheses?
The approximate statistical test to compare the population mean to a hypothesized value (zero), when the population standard deviation is unknown would be "One Sample Test"
j. What is the null distribution of this test statistic?
The test statistic for the t test would be given by giving 1.73
k. What is the decision rule that might be used here (use α = 0.10)?
l. What decision was made with regard to the null hypothesis?
m. What is your conclusion based on the available data?
n. What is your best point estimate of the average error for the National Park Service’s predictions?
o. Provide a 90% confidence interval for the average prediction error for the National Park Service’s estimated eruption times.
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?
Hi! Thank you for the question, As per the honor code, we are allowed to answer three sub-parts at a time so we are answering the first three as you have not mentioned which of these you are looking for. Please re-submit the question separately for the remaining sub-parts.
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