5. A particular line of business has three types of claims. The historical probability and thenumber of claims for each type in the current year are:ТуреHistorical ProbabilityNumber ofClaims inCurrent YearA0.2744112B0.35121800.3744138Calculate the chi-square goodness-of-fit test statistic.b. Compute the p-value.c. What can you conclude? (Given a =a.= 0.05)

Below is the following table : Categories Observed Expected (fo-fe)2/fe A 112…

Answered: a. Calculate the chi-square…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

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5. A particular line of business has three types of claims. The historical probability and the
number of claims for each type in the current year are:
Туре
Historical Probability
Number of
Claims in
Current Year
A
0.2744
112
B
0.3512
180
0.3744
138
Calculate the chi-square goodness-of-fit test statistic.
b. Compute the p-value.
c. What can you conclude? (Given a =
a.
= 0.05)

Expert Solution

Step 1

Below is the following table :

Categories	Observed	Expected	(fo-fe)²/fe
A	112	430*0.2744=117.992	(112-117.992)²/117.992 = 0.304
B	180	430*0.3512=151.016	(180-151.016)²/151.016 = 5.563
C	138	430*0.3744=160.992	(138-160.992)²/160.992 = 3.284

Sum =	430	430	9.151

Null and Alternative Hypotheses

The following null and alternative hypotheses need to be tested:

$H_0: p_1 = 0.2744, p_2 = 0.3512, p_3 = 0.3744$

$H_a$ : Some of the population proportions differ from the values stated in the null hypothesis

a) This corresponds to a Chi-Square test for Goodness of Fit.

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