1)write the name of the test you will conduct,

2)state the hypotheses,

3)conduct the test,

4)state your decision alongside your statistical statement of significance

5)measure effect size whenever applicable using all available measures

6)write a conclusion 

Thanks!

Problem: A researcher wanted to find out if there is a difference in how often elderly people who own dogs visit their doctors after upsetting events compared those who do not own dogs. To answer this question, a sample of elderly dog owners was compared to elderly who do not own dogs. The researcher recorded the number of visits to the doctor during the past year for each person. Is there a significant difference in the number of doctor's visits for elderly who own or do not own dogs? Test at the .05 significance level.

Control group (not dog owners): 12, 10, 6, 9, 15, 12, 14

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

(1) we use t test for independent

(2) Ho: u1 - u2 =0 ; H1: u1 - u2 ≠ 0

(3) test statistic: 3.1878

(4) we reject Ho, p-value: 0.01

(5) effective size = 1.7428

(6) there is significant difference in the number of doctor's visits for elderly who own or do not own dogs

Step-by-step explanation

Given that,

sample-1 : (12 , 10 , 6 , 9 , 15 , 12 , 14 )

mean(x)=11.1429

standard deviation , s.d1=3.0783

number(n1)=7

sample-2 : (8 , 5 , 9 , 4 , 6 )

mean(y)=6.4

standard deviation, s.d2 =2.0736

number(n2)=5

null, Ho: u1 - u2 =0

alternate, H1: u1 - u2 ≠ 0

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

level of significance, alpha = 0.05

degrees of freedom(df) = ( sd1 ^2 / n1 + sd2 ^2 /n2 )^2 / (s1^4 / n1^2 ( n1-1)) + (s2^4 / n2^2 ( n2-1))

df = (( (3.0783^2/7)+(2.0736^2/5) ))^2 / (( 3.0783^4 / (7^2 ( 7 - 1 )) ) + (2.0736^4/(5^2(5-1))))

df = 9.9945 ~10

from standard normal table, two tailed t alpha/2 =2.2281

since our test is two-tailed,

reject Ho, if to < -2.2281 OR if to > 2.2281

we got |to| = 3.18778 & | t alpha | = 2.2281

make decision

hence value of | to | > | t alpha| and here we reject Ho

p-value: two tailed ( double the one tail ) - Ha : ( p ≠ 3.1878 ) = 0.01

hence value of p0.05 > 0.01,here we reject Ho

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effective size = X1 - X2 /sqrt( Sp^2)

calculate pooled variance s^2= (n1-1*s1^2 + n2-1*s2^2 )/(n1+n2-2)

s^2 = (6*9.47593089 + 4*4.29981696) / (12- 2 )

s^2 = 7.40548532

effective size = (11.1429-6.4)/sqrt(7.40548532)

effective size = 1.7428