A researcher studying ADHD among teenagers obtains a simple

A researcher studying ADHD among teenagers obtains a simple random sample of 100 teenagers aged 13 to 17 and asks them whether or not they have ever been prescribed medication for ADHD. To say that the distribution of p-hat, the sample proportion of teenagers who respond no, is approximately normal, how many more teengagers aged 13 to 17 does the researcher need to sample if

a) 90% of all teenagers aged 13 to 17 have never been prescribed medication for ADHD?

b) 95% of all teenagers aged 13 to 17 have never been prescribed medication for ADHD?

Solution

we know that the sampling distribution of p-hat i.e,proportion of teenagers who respond no , is approximately normal.....
Now, for a simple random smaple with sample size = n and popltn proportion = p..the sampling distribution of p-hat is approximately normal when .......

n*p*(1 - p) >=10....

a) p =0.9....n = requirred sample size...
so , n* ( 09 * 0.1 ) >=10...

n >= 111.1111

so, minimum sample size = 112...so, we need atleast 12 more teenagers in the sample.....

b) p =0.95..

so, n* .95 * 0.05 >= 10

or, n >=  210.5263
so, mimimum sample size = 211...so, we need atleast 111 more teenagers in our sample......