Medical researchers in a certain country followed 6378 men for 30 years to see i
ID: 3296233 • Letter: M
Question
Medical researchers in a certain country followed 6378 men for 30 years to see if there was any association between the amount of fish in their diet and prostate cancer. The medical researchers had a vested interest in presenting unblased data. The data are provided in the acoompanying table. Complete parts a through d below Click the icon to view the data table. Check the assumptions and conditions. Determine if all the assumptions and conditions have been met and if not, which ones have not been met The Counted Data Condition The Randomization Condition The Expected Cell Frequency Condition Find the value of the teet statistic and is necessary and is not satisfied is necessary and is satisfied. (Round to two decimal places as P-value-(Round to three decimal pu Click to select your answers). is not necessary.
Explanation / Answer
a. Prospective study is all about observing a cohort of subjects for a long period to study a particular disease or any outcome and relates it to other factors, wheras, retrospective study looks back to any outcome and relates factors to it. Thus the former is forward based, and later is backward based. This is a prospective study as the subjects were observed for a long period (30 years) to see if prostrate cancer is related to amount of fish in their diet.
b. When the data are categories of a single variable gathered from more than one group, one wonders whether the groups are the same; the question is homogeneity. When the data cross categorize two variables gathered from single group, one wonders whether there is an association; the question is independence. Thus, this is a test of independence, as the data count sof individual men categorized into two variables-consumption of fish and prostrate cancer. [Please note: options are not readable as pop up window is blocking them].
c. Test statistic.
X^2=sigma (fo-fe)^2/fe
=1.616~1.62(ans)
p value at 3 [(2-1)*(4-1)] degrees of freedom is 0.656.
Per rejection rule based on p value, reject null hypothesis if p value is less than alpha. Here, p value is not less than 0.05, therefore, fail to reject null hypothesis. There is insufficient sample evidence that eating fish and prostrate cancer are related.
This study does not prove that eating fish affects prostrate cancer as the null hypothesis is not rejected, which proves there is no relationship.
Observed,fo Expected, fe=(row marginal*column marginal)/Total] (Observed-Expected)^2/Expected 11 9.8 [(131*479)/6378] 0.13716 [(11-9.8)^2/9.8] 120 121.2 0.01114 204 199.1 0.12083 2447 2451.9 0.00981 215 226.4 0.57720 2800 2788.6 0.04687 49 43.6 0.65984 532 537.4 0.05358X^2=sigma (fo-fe)^2/fe
=1.616~1.62(ans)