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In: Statistics and Probability

1. Research has shown that elderly people who owned dogs were less likely to pay visits...

1. Research has shown that elderly people who owned dogs were less likely to pay visits to their doctors after upsetting events than were those who did not own pets. Similarly, consider the following hypothetical data. A sample of elderly dog owners is compared to a similar group (in terms or age and health) who do not own dogs. The researcher records the number of visits to the doctor during the past year for each person. The data are as follows:

Dog Owners: 8,5,9,4,6

Control Group: 12, 10 , 6, 9, 15, 12 , 14

a) Is there a significant difference in the number of doctor visits between dog owners and control subjects? Use a two-tailed test with α = .05.

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Expert Solution

Answer:

Given that:

The researcher records the number of visits to the doctor during the past year for each person. The data are as follows:

Dog Owners: 8,5,9,4,6

Control Group: 12, 10 , 6, 9, 15, 12 , 14

a)  Is there a significant difference in the number of doctor visits between dog owners and control subjects? Use a two-tailed test with α = .05



mean(x)=11.1429


standard deviation , s.d1=3.0783


number(n1)=7


y(mean)=6.4


standard deviation, s.d2 =2.0736


number(n2)=5


null, Ho: u1 = u2


alternate, H1: u1   u2


level of significance, α = 0.05


from standard normal table, two tailed t α/2 =2.776


since our test is two-tailed
reject Ho, if to < -2.776 OR if to > 2.776


we use test statistic (t) = (x-y)/sqrt(s.d1^2/n1)+(s.d2^2/n2)


to =11.1429-6.4/sqrt((9.47593/7)+(4.29982/5))


to =3.1878


| to | =3.1878


critical value
the value of |t α| with min (n1-1, n2-1) i.e 4 d.f is 2.776
we got |to| = 3.18778 & | t α | = 2.776


make decision
hence value of | to | > | t α| and here we reject Ho
p-value: two tailed ( double the one tail ) - Ha : ( p != 3.1878 ) = 0.033
hence value of p0.05 > 0.033,here we reject Ho


ANSWERS:
---------------
null, Ho: u1 = u2
alternate, H1: u1 != u2
test statistic: 3.1878
critical value: -2.776 , 2.776
decision: reject Ho
p-value: 0.033
we have enough evidence to support the claim that difference of number of doctors visits
between dog owners and control subjects.

orchestra answered 2 years ago
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