A recent study of undergraduates looked at gender differences in dieting trends.
ID: 3359432 • Letter: A
Question
A recent study of undergraduates looked at gender differences in dieting trends. There were 189 women and 104 men who participated in the survey. The table below summarizes whether a student tried a low-fat diet or not by gender:
(a) Fill in the missing cells of the table. (The ones with question marks)
(b) Summarize the data numerically. What percent of each gender has tried low-fat diets? (Round your answers to two decimal places.)
(c) Test that there is no association between gender and the likelihood of trying a low-fat diet. (Round your 2 to three decimal places, and round your P-value to four decimal places.)
Explanation / Answer
Given table data is as below
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calculation formula for E table matrigender
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egenderpected frequecies calculated blikelihood appllikelihood ing E - table matrigender formulae
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calculate chisquare test statistic using given observed frequencies, calculated egenderpected frequencies from above
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set up null vs alternative as
null, Ho: no relation b/w gender and likelihood OR gender and likelihood are independent
alternative, H1: egenderists a relation b/w gender and likelihood OR gender and likelihood 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 = 7.8108
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| =7.8108 & | ^2 | =3.8415
make decision
hence value of | ^2 o | > | ^2 | and here we reject Ho
^2 p_value =0.0052
ANSWERS
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null, Ho: no relation b/w gender and likelihood OR gender and likelihood are independent
alternative, H1: egenderists a relation b/w gender and likelihood OR gender and likelihood are dependent
test statistic: 7.8108
critical value: 3.8415
p-value:0.0052
decision: reject Ho
col1 col2 TOTALS 38 8 46 151 96 247 189 104 N = 293