Problem 3 (each 5 points) 349 stuuly there were S1 colorectal who did not suheeq

Question

Problem 3 (each 5 points) 349 stuuly there were S1 colorectal who did not suheequently use aspirin, article " Aspirin Use and Survival After Dingnosis of Colorectal Cancer" reported that of pants who regularly used aspirin alter being dinguosed with colorectal cancer citic deaths, whereas among 730 similarly diagnosed individuals there werte 141 colorectal deaths Does this data suggest that t the regular use of aspirin after diagnosis will decreases the incidence rate of colorectal o cancer-specitic deaths a) State the Null and Alternative hypothesis. b) Draw the picture to state the rejection region for a significance level of 0.05. c) Find the Test statistic value a d) Find the P-value. e) Decide whether Ho should be rejected.

Explanation / Answer

p1 = 81/649 = 0.125

p2 = 141/730 = 0.193

H0: p1 = p2

H1: p1 < p2

The pooled sample proportion (P) = (p1 * n1 + p2 * n2)/(n1 + n2) = (0.125 * 649 + 0.193 * 730)/(649 + 730)

= 0.16

SE = sqrt(P * (1 - P) * (1/n1 + 1/n2))

= sqrt (0.16 * 0.84 * (1/649 + 1/730))

= 0.02

The test statistic Z = (p1 - p2)/SE

= (0.125 - 0.193)/0.02

= -3.4

P-value = P(Z < -3.4)

= 0.0003

As the p-value is less than the significance level 0.05, so the null hypothesis is rejected.

So there is sufficient evidence to support that the regular use of aspirin after diagnosis will decreases the incidence of cholesterol cancer specific deaths.

  

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