9. A random sample of 235 people was collected. We would like to determine if th

Question

9. A random sample of 235 people was collected. We would like to determine if there is a relationship between exposure to the flu, and whether or not they contracted the flu. Use tbe 2x 2 contingency table below to answer the following questions 35 Not Contracted125 70 (a) Compute P(Contracted) (b) Compute P(Contracted | Exposed) (e) Based on this, does it appear that the variables are independent? Why or why not? (d) State the null and alternative bypothesis for Pearson's chi-squared test of independence. (e) Find the test-statistic for this test. (f) Find the p-value for this test (8) Should we reject or fail to reject the null hypothesis?

Explanation / Answer

a)
P(contracted) = (35 + 5)/235
=40/235=0.170212
b)
P(contracted|exposed) = 35/(35 + 125) = 35/160 = 0.21875
c)
No
as P(contracted) is not equal to P(contracted|exposed)
d)
Null : both variable are independent
Alternate : both are not independent

e)

TS = 8.362146

f)

p-value = 0.003831178

g)

we reject the null as p-value < 0.05

c1 c2 total r1 35 5 40 r2 125 70 195 total 160 75 235 Oi 35 5 125 70 Ei 27.23404 12.76596 132.766 62.23404 TS (O--Ei)^2/Ei 2.214511 4.724291 0.454259 0.969085 8.362146 critical value 3.84 p-value 0.003831178

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