A restaurant manager is interested in investigating whether the main course orde
ID: 3320803 • Letter: A
Question
A restaurant manager is interested in investigating whether the main course ordered and the dessert ordered are dependent. The table below shows the results of a survey.
What can be concluded at the 0.05 level of significance?
The p-value is:
p-Value = [ Select ] ["0.016", "0.271", "0.027", "0.044"]
Conclusion:
[ Select ] ["There is insufficient evidence to support the claim that main course and dessert ordered are dependent.", "There is sufficient evidence to support the claim that main course and dessert ordered are dependent."]
Fish Meat Vegetarian Cake 41 68 19 Ice Cream 62 99 54 Pie 59 104 25Explanation / Answer
There is sufficient evidence to support the claim that main course and dessert ordered are dependent
Given table data is as below MATRIX col1 col2 col3 TOTALS row 1 41 68 19 128 row 2 62 99 54 215 row 3 59 104 25 188 TOTALS 162 271 98 N = 531 ------------------------------------------------------------------calculation formula for E table matrix E-TABLE col1 col2 col3 row 1 row1*col1/N row1*col2/N row1*col3/N row 2 row2*col1/N row2*col2/N row2*col3/N row 3 row3*col1/N row3*col2/N row3*col3/N ------------------------------------------------------------------
expected frequecies calculated by applying E - table matrix formulae E-TABLE col1 col2 col3 row 1 39.051 65.326 23.623 row 2 65.593 109.727 39.68 row 3 57.356 95.947 34.697 ------------------------------------------------------------------
calculate chisquare test statistic using given observed frequencies, calculated expected frequencies from above Oi Ei Oi-Ei (Oi-Ei)^2 (Oi-Ei)^2/Ei 41 39.051 1.949 3.799 0.097 68 65.326 2.674 7.15 0.109 19 23.623 -4.623 21.372 0.905 62 65.593 -3.593 12.91 0.197 99 109.727 -10.727 115.069 1.049 54 39.68 14.32 205.062 5.168 59 57.356 1.644 2.703 0.047 104 95.947 8.053 64.851 0.676 25 34.697 -9.697 94.032 2.71 ^2 o = 10.958 ------------------------------------------------------------------
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 =9.488
since our test is right tailed,reject Ho when ^2 o > 9.488
we use test statistic ^2 o = (Oi-Ei)^2/Ei
from the table , ^2 o = 10.958
critical value
the value of |^2 | at los 0.05 with d.f (r-1)(c-1)= ( 3 -1 ) * ( 3 - 1 ) = 2 * 2 = 4 is 9.488
we got | ^2| =10.958 & | ^2 | =9.488
make decision
hence value of | ^2 o | > | ^2 | and here we reject Ho
^2 p_value =0.027
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: 10.958
critical value: 9.488
p-value:0.027
decision: reject Ho