Answered: Park officials make predictions of…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

See similar textbooks

Related questions

Question

Park officials make predictions of times to the next eruption of a particular geyser, and collect data for the errors (minutes)in those predictions. The display from technology available below results from using the prediction errors to test the claim that the mean prediction error is equal to zero. Comment on the accuracy of the predictions. Use a 0.05 significance level. Identify the null and alternative hypotheses, test statistic, P-value, and state the final conclusion that addresses the original claim.

A. Identify the test statistic.

(Round to two decimal places as needed.)

B. Identify the P-value.

(Round to three decimal places as needed.)

### Statistical Analysis Summary

- **Difference**: −0.536
- **t (Observed value)**: −7.61
- **| t | (Critical value)**: 1.985
- **DF (Degrees of Freedom)**: 96
- **p-value (Two-tailed)**: <0.0001
- **alpha (Significance Level)**: 0.05

This data set provides results from a t-test. The observed t value is −7.61, which is significantly different from the critical value of 1.985 at 96 degrees of freedom. With a two-tailed p-value of less than 0.0001, the result is statistically significant at an alpha level of 0.05. This indicates strong evidence against the null hypothesis.

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 + ...

Expert Solution