Question

2. An environmentalist is interested in estimating the mean time between 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.

Time Between Eruptions (in minutes)
63 63 71 77 81 65
67 84 72 75 70 70
93 83 85 79 90 74
81 74 80 65 70 84
83 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
97 93 73 81 85 90
(a) Construct a stem-and-leaf diagrams of the times using two lines per stem.
(b) Describe the stem-and-leaf diagram. When describing a graph, you must describe the shape,
center and spread.
(c) Form a 95% confidence interval for the mean time between all eruptions of Old Faithful
Geyser. Use clear, complete sentences to interpret the interval.
Confidence Interval
(d) Based on the 95% confidence interval formed in part (c), is it plausible that the mean time
between all eruptions of Old Faithfull geyser is 77 minutes? Why or why not? Use clear,
complete sentences to state and justify your answer.
(e) Based on the 95% confidence interval formed in part (c), is it plausible that the mean time
between all eruptions of Old Faithfull geyser is 90 minutes? Why or why not? Use clear,
complete sentences to state and justify your answer.

Answer 1

a.)

b)

By looking into above plot we can approximate that the shape or distribution of the given data is approximately Normally distributed, and center of the data can be consider as 77 (center means here half of the data are below 77 and half of the data are above 77), spread of the data will be between 57 and 59.

c.)

n=60

degree of freedom=n-1=59

we are 95% confidence that the true maen will lie between the rage 74.92 and 80.02.

d.)Yes it is plausible that the mean time between all eruptions of Old Faithfull geyser is 77 minutes, because the 95% confidence interval consists the mean value77.

e.)

No. It is not  it plausible that the mean time between all eruptions of Old Faithfull geyser is 90 minutes,because 95% confidence interval does not consists the mean value 90.