+ Cone of the I arour (8 points) 2. An environmentalist is interested in estimating the mean time between ALL Problem continued from last page... eruptions of Old Faithful Geyser in Yellowstone National Park. Over the course of a year, she takes a random sample of the time intervals (in minutes) between eruptions. Her results are recorded in the following table. Both the population mean and standard deviation are unknown. be specific. (c) Define the parameter of interest, using proper notation. Use a clear, complete sentence and Time Between Eruptions (in minutes) 77 81 63 63 71 65 67 84 72 75 70 70 79 93 83 85 90 74 65 81 74 80 70 using proper notation. 84 (d) Use the information from the sample to give the best estimate of the population parameter, 78 71 67 97 88 62 61 57 86 70 77 78 75 67 89 93 81 86 65 70 77 83 76 76 67 99 75 76 83 93 73 85 97 90 (e) Form a 95% confidence interval for the mean time between all eruptions of Old Faithful Geyser. Use clear, complete sentences to interpret the interval. (a) Construct a stem-and-leaf diagrams of the times using two lines per stem. Confidence Interval stem leaf 1233 55 5 777 7 0 0 0 0 0 | 12344 5 5 5 6 6 4 7 7 7 8 8 9 (f) Based on the 95% confidence interval formed in part (c), is it plausible that the mean time 01 1 1 13 3 3 3 44 between all eruptions of Old Faithfull geyser is 100 minutes? Why or why not? Use clear, complete sentences to state and justify your answer. 5 5 6 6 8 9 103 3 3 77 9 b) Describe the stem-and-leaf diagram. When describing a graph, you must describe the shape, enter and spread. (g) Based on the 95% confidence interval formed in part (c), is it plausible that the mean time based on the Stem and leaf diagram the median Is 77 , between all eruptions of Old Faithfull geyser is 76 minutes? Why or why not? Use clear, complete sentences to state and justify your answer. alf of the data is below 77 and half is above 77 . Therefore the rape of the distribution is bell shaped or symmetric . The stribution is unimodal . There is no butler In given distribute blem continued on next page