SGD Statistical Analysis

In the study on the effect of dental hygiene instruction on the subsequent occurrence of dental caries in children, $100$ children were randomly selected from the patient population of a pediatric dental clinic. $50$ children were randomly selected to receive instruction in dental hygiene and $50$ were randomly designated to the control $($no instruction$)$ group. Six months later, the number of new cavities was tabulated for each child. The results are summarized below:

$\backslash$table$[[,$Number of New Cavities$],[,0-1,2-3,4-5,$Totals$],[$Instruction$,30,15,5,50],[$No Instruction,$20,15,15,50],[$Total$,50,30,20,100]]$

a$.$ What type of design was used?

b$.$ Test the hypothesis that dental hygiene instruction is related to the number of new cavities occurring during the succeeding six months at the $=\mathrm{.}05$ level of significance. Follow the steps of hypothesis testing.

c$.$ Report and interpret the p$-$value.

$2.$ The table below depicts the data on a food poisoning outbreak following a back$-$to$-$school party attended by $200$ medical students.

$\backslash$table$[[$Ate Food,Did Not Ate Food$],[,$III,Not III,Totals,III,Not III,Totals$],[$Barbecue$,90,30,120,20,60,80],[$Cole Slaw,$67,33,100,43,57,100],[,157,63,220,63,117,180]]$

a$.$ What is the RR of developing food poisoning after barbecue consumption?

b$.$ What is the RR of developing food poisoning after eating coleslaw?

c$.$ Interpret your results.

$3.$ To study the possible association between oral contraceptive use and the occurrence of Rheumatoid Arthritis $($RA$),$ an investigator selected $100$ women with a confirmed diagnosis of RA and $200$ women undergoing treatment at the same medical facility for other musculoskeletal conditions as subjects. The medical records of all subjects $($prior to the date of first diagnosis$)$ were reviewed for evidence of oral contraceptive use. The table below show the results.

$\backslash$table$[[,$Rheumatoid Arthritis$],[$Oral Contraceptive Use,Present,Absent,Totals$],[$User$,40,120,160],[$Non$-$User,$60,80,140],[$Totals$,100,200,300]]$

a$.$ What type of study design was employed?

b$.$ Calculate and interpret the OR$.$

c$.$ Can RR be directly calculated from the results of this study? Why?

d$.$ Is there a statistically significant association between oral contraceptive use and occurrence of rheumatoid arthritis?