Answered: ) Which of the following figures (next…

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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Question

Suppose that a recent article by a historian stated that the mean time spent in jail by a first–time
convicted burglar in the 20th century was 2.5 years. A study was then done to see if the mean time has increased
in the new century. A random sample of 26 first-time convicted burglars in a recent year was picked. The mean
length of time in jail from the survey was 3 years. Suppose that it is somehow known that the population standard
deviation is 1.8 years and that the population is normally distributed.
The hypotheses can then be framed as:
H0 : μ = 2.5 vs. Ha : μ > 2.5
(a) Which of the following figures (next page) best describes the p-value for this hypothesis testing
problem. Explain your reasoning. (numbers above red shaded area represent the corresponding probabilities).

(b) Write the decision and conclusion for this hypothesis testing problem if the significance level, α,
is 0.1.