Some sociologists suspect that highly publicized suicides may trigger additional

Question

Some sociologists suspect that highly publicized suicides may trigger additional suicides. In one investigation of this hypothesis, D.P. Phillips collected information about 17 airplane crashes that were known (because of notes left behind) to be murder–suicides. For each of these crashes, Phillips reported an index of the news coverage (circulation of nine newspapers devoting space to the crash multiplied by length of coverage) (“Index”) and the number of multiple-fatality plane crashes (“Crashes”) during the week following the publicized crash

Index of coverage # of Crashes

376, 8

347, 5

322, 8

104, 4

103, 6

98, 4

96, 8

85, 6

82, 4

63, 2

44, 7

40, 4

5, 3

5, 2

0, 4

0, 3

0, 2

Using all necessary steps, fit, evaluate and interpret (if deemed appropriate) a statistical model to evaluate if the sociologists’ hypothesis is correct, and that the “Index” variable is related to the number of multiple-fatality plane crashes.

Explanation / Answer

Given that,
mean(x)=104.1176
standard deviation , s.d1=123.2498
number(n1)=17
y(mean)=4.7059
standard deviation, s.d2 =2.1144
number(n2)=17
null, Ho: u1 = u2
alternate, H1: u1 != u2
level of significance, = 0.05
from standard normal table, two tailed t /2 =2.12
since our test is two-tailed
reject Ho, if to < -2.12 OR if to > 2.12
we use test statistic (t) = (x-y)/sqrt(s.d1^2/n1)+(s.d2^2/n2)
to =104.1176-4.7059/sqrt((15190.5132/17)+(4.47069/17))
to =3.325
| to | =3.325
critical value
the value of |t | with min (n1-1, n2-1) i.e 16 d.f is 2.12
we got |to| = 3.32515 & | t | = 2.12
make decision
hence value of | to | > | t | and here we reject Ho
p-value: two tailed ( double the one tail ) - Ha : ( p != 3.3252 ) = 0.004
hence value of p0.05 > 0.004,here we reject Ho
ANSWERS
---------------
null, Ho: u1 = u2
alternate, H1: u1 != u2
test statistic: 3.325
critical value: -2.12 , 2.12
decision: reject Ho
p-value: 0.004

we have enough evidence to support the claim that the Index variable is related to the number of multiple-fatality plane crashes.

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