Old Faithful is a geyser located in Yellowstone National Park in Wyoming, USA. Millions of travelers come from afar to witness Old Faithful's eruptions each year. Travelers to Yellowstone are told that Old Faithful is expected to erupt, on average, every 7272 minutes, but park scientists suspect that this average is incorrect. To investigate, the scientists determine the waiting time until the next eruption for a random sample of 272272 Old Faithful eruptions. The waiting times have a mean of 70.897 minutes and a standard deviation of 13.595 minutes. You will use these data to carry out a significance test at the ?α = 0.05 level. PLAN: One-sample t test for µ. Select 2 correct statements.Random: A random sample of eruptions are selected.Random: This condition is not met.Normal/Large Sample: n = 272 is large (>30)Normal/Large Sample: This condition is not met.DO: Enter the test statistic to 2 decimal places and enter the P-value to 4 decimal places. (Use technology)t-statistic(Round to 2 decimal places)P-value =(Use technology. Round to 4 decimal places)CONCLUDE:Based on the P-value, what can you conclude about the park scientists' claim that the average time between eruptions of OldFaithful differs from 72?The correct decision is tothe null hypothesis because there isat the= 0.05 level that the mean waiting times until the next eruption are different than previously claimed.a =

The random variable waiting time follows normal distribution. We have to test whether the mean…

Answered: Old Faithful is a geyser located in…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Old Faithful is a geyser located in Yellowstone National Park in Wyoming, USA. Millions of travelers come from afar to witness Old Faithful's eruptions each year. Travelers to Yellowstone are told that Old Faithful is expected to erupt, on average, every 7272 minutes, but park scientists suspect that this average is incorrect.

To investigate, the scientists determine the waiting time until the next eruption for a random sample of 272272 Old Faithful eruptions. The waiting times have a mean of 70.897 minutes and a standard deviation of 13.595 minutes. You will use these data to carry out a significance test at the ?α = 0.05 level.

PLAN: One-sample t test for µ. Select 2 correct statements.
Random: A random sample of eruptions are selected.
Random: This condition is not met.
Normal/Large Sample: n = 272 is large (>30)
Normal/Large Sample: This condition is not met.
DO: Enter the test statistic to 2 decimal places and enter the P-value to 4 decimal places. (Use technology)
t-statistic
(Round to 2 decimal places)
P-value =
(Use technology. Round to 4 decimal places)
CONCLUDE:
Based on the P-value, what can you conclude about the park scientists' claim that the average time between eruptions of Old
Faithful differs from 72?
The correct decision is to
the null hypothesis because there is
at the
= 0.05 level that the mean waiting times until the next eruption are different than previously claimed.
a =

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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