On November 15 - 18, 2012 Gallup conducted a survey of 1,015 randomly selected U
ID: 3319216 • Letter: O
Question
On November 15 - 18, 2012 Gallup conducted a survey of 1,015 randomly selected U.S. adults about "Black Friday" shopping. They asked the following question:
"As you know, the Friday after Thanksgiving is one of the biggest shopping days of the year.
Looking ahead, do you personally plan on shopping on the Friday after Thanksgiving, or not?"
Their results, broken down by sex, are summarized in the provided two-way table.
Yes Shopping
No Shopping
Total
82
433
515
100
400
500
182
833
1,015
Test, at the 1% level, if there is a significant association between sex and plans to shop the Friday after Thanksgiving. Include all details of your test.
Yes Shopping
No Shopping
Total
Male82
433
515
Female100
400
500
Total182
833
1,015
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, 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
level of significance, = 0.05
from standard normal table, chi square value at right tailed, ^2 /2 =3.8415
since our test is right tailed,reject Ho when ^2 o > 3.8415
we use test statistic ^2 o = (Oi-Ei)^2/Ei
from the table , ^2 o = 2.8665
critical value
the value of |^2 | at los 0.05 with d.f (r-1)(c-1)= ( 2 -1 ) * ( 2 - 1 ) = 1 * 1 = 1 is 3.8415
we got | ^2| =2.8665 & | ^2 | =3.8415
make decision
hence value of | ^2 o | < | ^2 | and here we do not reject Ho
^2 p_value =0.0904
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: 2.8665
critical value: 3.8415
p-value:0.0904
decision: do not reject Ho
Hence we don't have evidence that there is a significant association between sex and plans to shop the Friday after Thanksgiving
col1 col2 TOTALS 82 433 515 100 400 500 182 833 N = 1015Related Questions
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