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There are four different clinical sites in a small city, patients in each site are enrolled and randomly receive either the experimental medication designed to

There are four different clinical sites in a small city, patients in each site are enrolled and randomly receive either the experimental medication designed to lower blood pressure or a placebo, then the patient's blood pressure is measured after 5 hours. Data is given in the following table:

Treatment Site 1 Site 2 Site 3 Site 4
Hypertensive 150 137 232 149
Non Hypertensive 136 195 234 100

(a) [2 marks] Test if there is a difference in the proportions of hypertensive patients across clinical sites. Run the Chi-Squared test at a 5\% level of significance and clearly state hypotheses, test statistics, p-value and conclusion.

( b) [2 marks] Partition Chi-square into components regarding the choice between Site 3 with a combination of Sites 1, 2, and 4 and then between Sites 1, 2, and 4. Interpret the results. (Write the hypotheses, test stat, p-value and conclusion for both analyses.)

( c) [2 marks] Fit the independent and saturated loglinear models for these data. Is there sufficient evidence to indicate that there is a relationship between treatment and site? Justify your answer.

(Add screenshots of Jamovi for all three parts if possible)

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