Question

There is concern that the Type 2 diabetes drug Avandia raises the risk of having a heart attack. The general population of people with Type 2 diabetes has a 20.2% chance of heart attack within 7 years. In a random sample of 4,485 people with Type 2 diabetes and who used Avandia, 28.9% of these individuals had a heart attack within 7 years. If researchers want to compute the z-test for this data, what assumption should they check?

A) because the sample size is large enough, they dont have to check any assumptions

B)They Need to check both 4485 x .202 and 4485 x (1-.202) are at least 10

Please explain

Answer 1

There is concern that the Type 2 diabetes drug Avandia raises the risk of having a heart attack. The general population of people with Type 2 diabetes has a 20.2% chance of heart attack within 7 years. In a random sample of 4,485 people with Type 2 diabetes and who used Avandia, 28.9% of these individuals had a heart attack within 7 years. If researchers want to compute the z-test for this data, what assumption should they check?

n = 4485

Sample proportion = 28.9%

np=1296.165

Since this a binomial proportion test because there are two outcomes of having a heart attack or not having heart attack.

We can use the normal approximation because of the following assumptions.

1. Sample size > 30 so it is large
2. np > 10

We need to check for both conditions and not just one.

Test

This is one tailed binomial proportion test since we want to check whether the proportion is greater than (null hypothesis) The drug is raising the chance so it should be tested whether its proportion is greater than older results.

: p = 20.2%

: p > 20.2%

Test Stat :

= 20.2%

Test Stat = 12.8534

Critical value :   Since level of significance is 0.05

=

= 1.6449 .............using normal percentage tables

Since |T.S.| > C.V.

We reject the null hypotheis at 5% level of significance. Therefore we concldue that the drugs significantly increase the chancesof attack.

A) because the sample size is large enough, they dont have to check any assumptions

Partly correct because np is also to be checked

B)They Need to check both 4485 x .202 and 4485 x (1-.202) are at least 10

Here we are not to check will null proportion but the sample proportion.