Help with exercise on parametric tests!

#1
Hello!
I'm really having a tough time with this exercise and I don't even know where I am supposed to start from! Could you help me?

There were 1000 citizens in a small town. Because of a disease, 811 of them got vaccinated. However, 200 citizens died and 110 of them were vaccinated.
(a) Test if the vaccine prevents death significantly
(b) Test if the vaccine increases the probability of surviving by more than 30 percentage points.

thank you!
 

Karabiner

TS Contributor
#2
For the start: Create a 2x2 contingency table like this one. You can insert the numbers which
you already have, and calculate the missing numbers. Then you can run tests for a) and b).

With kind regards

Karabiner
 
#3
I did. What I did so far is:

Hypoteses: H0: PA = PB H1: PA < PB

With PA: probability of death for those vaccines (110/811 = 0.135) and PB: probability of death for those non vaccined (90/189 = 0.476)

And then probability of death PD = 110+90/1000 = 0,2

Then, I calculated the z score with a formula the professor gave us but I'm not sure if I chose the right one. I got that the z score is -10,55.

But I don't know how to move from here.. the z score seems so high and I can't find the p value..
 

Karabiner

TS Contributor
#4
If you have a z score, normally you can find the according p-value by using a z table.

A z value of -10 seems uncommonly large, though, therefore I don't know whether you chose the
correct formula.

Personally, for (a) I would have simply used a Chi² test.

With kind regards

Karabiner
 
#5
I used this formula for the z score: z = (PA-PB)-0.30/sqrt P(1-P)(1/NA + 1/NB) with PA and PB probability of death and NA total people who died among those vaccines and NB total people who died among no vax