Question

4. The results of testing a new drug on 1,000 people with a certain disease found that 510 of them improved when they used the drug. Assume these 1,000 people can be regarded

as a random sample from the population of all people with this disease. Based on these results, would it be reasonable to think that more than half of the people with this disease would
improve if they used the new drug? Why or why not?

Answer 1

It would not be reasonable to say that more than half of the people with this disease would improve if they used the new drug

Explanation:

Data provided in the question:

Sample size, n = 1000

Number of people improved when they used the drug = 510

Thus,

Probability that Number of people improved when they used the drug

= 510 ÷ 1000

= 0.510

Now,

margin of error, E =
`2*\sqrt{(p(1-p))/(n)}`

=
`2*\sqrt{(0.510(1-0.510))/(1000)}`

= 0.032 = 3.2%

Therefore,

Portion of 0.510 is likely to lie in the 3.2% of the actual value of population

And,

The lower portion can be as small as p - E

= 0.510 - 0.032

= 0.478 i.e 47.8% of the sample

Hence,

It would not be reasonable to say that more than half of the people with this disease would improve if they used the new drug