A researcher is interested in the effect that exercise and gender may have an LD

Question

A researcher is interested in the effect that exercise and gender may have an LDL (BAD) cholesterol level . the researcher have data that classifies individuals,who are on a similar diet , by gender (male or female) and level of exercise is adequate or inadequate.

a) suppose that the mean cholesterol levels repreesent the population ( so any effect is real and no significance testing is necessary )

adequate inadequate

male 180 220

female 165 ?

if there is no interaction between these two factors ,what would the missing mean cholesterol level be (i.e, for females who get inadequate exercise )?Explain yur answer.

b) interpret the main effects in part (a) above.

c) suppose that the following mean cholesterol levels represent the population (so any effect is real and no significance testing is necessary)

adequate inadequate

male 180 220

female 165 230

explain which effects are preesent and fully interpret these effects as appropriate . based on these results , what overall conclusions can be drawn about the effect of exercise and gender on LDL cholesterol?

Explanation / Answer

(a) Answer : Let say that the missing value is d

so as there is no asssociation between these two factors.

(Adequate - Male) * (inadequate - female) = (inadequate -male) * (adequate - female)

180 * d = 220 * 165

d = 220 * 165 /180 = 201.67

It can be explained as such that the ratio of adequate people in all people shall be constant for both the genders.

(b) Here there is no relationship between gender and lower HDL levels. There are lower cholestrol level for adequate number of males and females. In females, it is more lower than male.

(c) Here chi-square tableis

Here X2 = 0.843

p - value = CHIINV( X2 > 0.843 ; 2) = 0.3585

so there is no significant effect of exercise and gender on LDL cholesterol.

Here Gamma distribution = ad/bc = (180 * 230)/ (165 * 220) = 1.14

so risk ratio is 1.14. So, the effects are not so significant in nature.

adequate inadequate Total male 180 220 400 female 165 230 395 Total 345 450 795 Expected adequate inadequate Total male 173.58 226.42 400 female 171.42 223.58 395 Total 345 450 795 Chi-square Table adequate inadequate Total male 0.237 0.182 0.419 female 0.240 0.184 0.424 Total 0.477 0.366 0.843

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