A study was conducted in 1000 people to test a new flu vaccine. Half of the part

Question

A study was conducted in 1000 people to test a new flu vaccine. Half of the participants were randomized to receive the old version of the vaccine (unexposed), and half of the participants were randomized to receive the new version of the vaccine (exposed). The participants were followed throughout the subsequent flu season. 200 people in the “old vaccine” group got the flu, whereas 300 people in the “new vaccine” group got the flu. Assume for this exercise that you cannot get flu more than once per season.

What type of study is this?

What measure of association should the investigators calculate?

Calculate this measure, rounded to 1 decimal place:

Does it appear, based on this study, that the old vaccine is more effective at preventing flu, or is the new vaccine more effective?

Explanation / Answer

Q.1 What type of study is this?

The study is a type of Observational study.

Q.2 What measure of association should the investigators calculate?

measures of association refer to a wide variety of coefficients that measure the statistical strength of the relationship on the variables of interest SO, here in this case we have to measure the effect of vacccine to the people statistically.

Calculate this measure, rounded to 1 decimal place:

Here H0 : pold = pnew

Ha : pold < pnew

where pold and pnew are the proportion of people who get affected by flue with old and new vaccine.

Pooled estimate p = (300 + 200)/ 1000 = 0.5

standrd error of the pooled proportion se= sqrt [p(1-p)/N] = sqrt [0.5 * 0.5 * (1/500 + 1/500) ] = 0.0316

so Z = (pnew - pold)/ se = ( 0.6 - 0.4)/ 0.0316 = 6.3

so Zcritical = 1.645 for alpha = 0.05

so here Z > Zcritical

Question 3 Does it appear, based on this study, that the old vaccine is more effective at preventing flu, or is the new vaccine more effective?

Answer : So, we can reject the null hypothesis and can claim that the he old vaccine is more effective at preventing flu.

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