Answered: A report classified fatal bicycle…

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

A report classified fatal bicycle accidents according to the month in which the accident occurred, resulting in the accompanying table.

Month	Number of Accidents
January	36
February	34
March	45
April	57
May	78
June	72
July	98
August	85
September	66
October	64
November	40
December	40

(a)

Use the given data to test the null hypothesis

H₀: p₁ =

, p₂ =

, , p₁₂ =

where

p₁

is the proportion of fatal bicycle accidents that occur in January,

p₂

is the proportion for February, and so on. Use a significance level of 0.01.

Calculate the test statistic. (Round your answer to two decimal places.)

χ² =

What is the P-value for the test? (Use a statistical computer package to calculate the P-value. Round your answer to four decimal places.)

P-value =

What can you conclude?

Do not reject H₀. There is not enough evidence to conclude that fatal bicycle accidents are not equally likely to occur in each of the months.Do not reject H₀. There is convincing evidence to conclude that fatal bicycle accidents are not equally likely to occur in each of the months. Reject H₀. There is not enough evidence to conclude that fatal bicycle accidents are not equally likely to occur in each of the months. Reject H₀. There is convincing evidence to conclude that fatal bicycle accidents are not equally likely to occur in each of the months.

(b)

The null hypothesis in part (a) specifies that fatal accidents were equally likely to occur in any of the 12 months. But not all months have the same number of days. What null and alternative hypotheses would you test to determine if some months are riskier than others if you wanted to take differing month lengths into account? (Assume this data was collected during a leap year, with 366 days.) (Enter your probabilities as fractions.)

Identify the null hypothesis by specifying the proportions of accidents we expect to occur in each month if the length of the month is taken into account. (Enter your probabilities as fractions.)

p₁= p₂= p₃= p₄= p₅= p₆= p₇= p₈= p₉= p₁₀= p₁₁= p₁₂=

Identify the correct alternative hypothesis.

H₀ is not true. None of the proportions is correctly specified under H₀.H₀ is true. At least one of the proportions is not correctly specified under H₀. H₀ is true. None of the proportions is not correctly specified under H₀. H₀ is not true. At least one of the proportions is not correctly specified under H₀.

(c)

Test the hypotheses proposed in part (b) using a 0.05 significance level.

Calculate the test statistic. (Round your answer to two decimal places.)

χ² =

What is the P-value for the test? (Use a statistical computer package to calculate the P-value. Round your answer to four decimal places.)

P-value =

What can you conclude?

Reject H₀. There is not enough evidence to conclude that fatal bicycle accidents do not occur in the twelve months in proportion to the lengths of the months. Reject H₀. There is convincing evidence to conclude that fatal bicycle accidents do not occur in the twelve months in proportion to the lengths of the months. Do not reject H₀. There is not enough evidence to conclude that fatal bicycle accidents do not occur in the twelve months in proportion to the lengths of the months.Do not reject H₀. There is convincing evidence to conclude that fatal bicycle accidents do not occur in the twelve months in proportion to the lengths of the months.

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