A research project based on a study of older adults examined the relationship be

Question

A research project based on a study of older adults examined the relationship between physical activity and pet ownership. The data collected included information concerning pet owner characteristics and the type of pet owned. Here are data giving the relationship between pet ownership status and gender.

Analyze the data. (Round your 2 to three decimal places and your P-value to four decimal places.)

Summarize your results and conclusions.(pick one)

The relationship between gender and pet ownership is not significant.

The relationship between gender and pet ownership is significant.   

Pet ownership status Gender      Non-pet owners      Dog owners      Cat owners Female      1028      158      85 Male      920      174      83

Explanation / Answer

Given table data is as below

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calculation formula for E table matrix

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expected frequecies calculaated 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, Ho: the relationship between gender and pet ownership is not significant.
alternative, H1: relationship between gender and pet ownership is significant
level of significance, = 0.05
from standard normal table, chi square value at right tailed, ^2 /2 =5.991
since our test is right tailed,reject Ho when ^2 o > 5.991
we use test statistic ^2 o = (Oi-Ei)^2/Ei
from the table , ^2 o = 3.177
critical value
the value of |^2 | at los 0.05 with d.f (r-1)(c-1)= ( 2 -1 ) * ( 3 - 1 ) = 1 * 2 = 2 is 5.991
we got | ^2| =3.177 & | ^2 | =5.991
make decision
hence value of | ^2 o | < | ^2 | and here we do not reject Ho
^2 p_value =0.204
ANSWERS
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null, Ho: the relationship between gender and pet ownership is not significant.
alternative, H1: relationship between gender and pet ownership is significant
test statistic: 3.177
critical value: 5.991
p-value:0.204
decision: do not reject Ho          

we claim that the relationship between gender and pet ownership is not significant.

col1 col2 col3 row 1 1028 158 85 1271 row 2 920 174 83 1177 TOTALS 1948 332 168 N = 2448

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