Many insurance companies are beginning to question the policy of offering reduce
ID: 3047828 • Letter: M
Question
Many insurance companies are beginning to question the policy of offering reduced rates to owners of subcompact cars because the companies claim that their rate of serious and fatal accidents is higher than that of owners of larger-sized cars. To investigate this issue, a researcher at the David Hughes Marketing Company made an analysis of accident data to determine the distribution of the numbers of cases in which at least one individual was either fatally or critically injured for automobiles of three sizes. The data for 346 accidents are shown below. Do these data indicate that the frequency of fatal and critical injuries in auto accidents depends on the size of automobiles? Use a = 0.10.
Size of Auto
Result Subcompact Compact Full Size
Fatal or critical injury 67 26 16
No fatal or critical injury 128 63 46
Explanation / Answer
Given table data is as below
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calculation formula for E table matrix
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expected frequecies calculated by applying E - table matrix formulae
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calculate chisquare test statistic using given observed frequencies, calculated expected frequencies from above
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set up null vs alternative as
null: the frequency of fatal and critical injuries independent on the size of automobiles.
alternative: the frequency of fatal and critical injuries dependent on the size of automobiles.
level of significance, = 0.1
from standard normal table, chi square value at right tailed, ^2 /2 =4.605
since our test is right tailed,reject Ho when ^2 o > 4.605
we use test statistic ^2 o = (Oi-Ei)^2/Ei
from the table , ^2 o = 1.886
critical value
the value of |^2 | at los 0.1 with d.f (r-1)(c-1)= ( 2 -1 ) * ( 3 - 1 ) = 1 * 2 = 2 is 4.605
we got | ^2| =1.886 & | ^2 | =4.605
make decision
hence value of | ^2 o | < | ^2 | and here we do not reject Ho
^2 p_value =0.389
ANSWERS
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null, Ho: no relation b/w X and Y OR X and Y are independent
alternative, H1: exists a relation b/w X and Y OR X and Y are dependent
test statistic: 1.886
critical value: 4.605
p-value:0.389
decision: do not reject Ho
fail to reject the null. The frequency of fatal and critical injuries does not depend on the size of automobiles
MATRIX col1 col2 col3 TOTALS row 1 67 26 16 109 row 2 128 63 46 237 TOTALS 195 89 62 N = 346Related Questions
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