Calculate the test statistic Calculate the p value What is the conclusion for this hypothesis test? What is the fundamental error with this analysis? A police department released the numbers of calls for the different days of the week during the month of October, as shown in the table to the right. Use a 0.01significance level to test the claim that the different days of the week have the same frequencies of police calls. What is the fundamental error with this analysis?DaySunMonTuesWedThursFriSatFrequency157201225249174205239

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Description: Calculate the test statistic Calculate the p value What is the conclusion for this hypothesis test? What is the fundamental error with this analysis? A police department released the numbers of calls for the different days of the week during the m

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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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Calculate the test statistic

Calculate the p value

What is the conclusion for this hypothesis test?

What is the fundamental error with this analysis?

A police department released the numbers of calls for the different days of the week during the month of October, as shown in the table to the right. Use a 0.01
significance level to test the claim that the different days of the week have the same frequencies of police calls. What is the fundamental error with this analysis?
Day
Sun
Mon
Tues
Wed
Thurs
Fri
Sat
Frequency
157
201
225
249
174
205
239

Expert Solution

Step 1

Let us first test whether “the different days of the week have the same frequencies of police calls”, using a Chi-square test of Goodness of fit.

Hypotheses:

The null hypothesis is:

H₀ : the different days of the week have the same frequencies of police calls.

The alternative hypothesis is:

H₁ : the different days of the week does not have the same frequencies of police calls.

Consider level of significance as 0.01.

Calculation steps:

The calculations have been done in EXCEL.

Denote O_i as the observed frequency (i =1, 2…7) and E_i as the expected frequency(i =1, 2…7). Here, the sample size, n=7.

The expected number of police calls for the day of the week is E_i=∑O_i/n. therefore, the value of the expected number of police calls will be (1,450)/7≈207.143.

Step 2

Test statistic:

The formula for the test statistic is χ² = ∑ [(O_i – E_i)² / E_i], summed over all i .

The Table calculates [(O_i – E_i)² / E_i]for each (i). So, the value in the first cell will be (157– 207.143)² /207.143 ≈ 1.6485.

The test statistic value can be calculated by adding all these cell values.

Day	Observed Frequency, Oi	Expected frequency, Ei	$\frac{(O i - E i)^{2}}{E i}$
Sun	157	207.143	12.1381
Mon	201	207.143	0.1822
Tue	225	207.143	1.5394
Wed	249	207.143	8.4580
Thurs	174	207.143	5.3029
Fri	205	207.143	0.0222
Sat	239	207.143	4.8994

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