Question

A researcher studying public opinion of proposed social security changes obtains a simple random sample of 5050 adult americans and asks them whether or not they support the proposed changes. to say that the distribution of the sample proportion of adults who respond? yes, is approximately? normal, how many more adult americans does the researcher need to sample in the following? cases? ?(a) 10?% of all adult americans support the changes ?(b) 15?% of all adult americans support the changes

Answer 1

We are given two scenarios
p = 10% = 0.10
and
p = 15% = 0.15

We are also given
n = 50 (it's not 5050 for this problem)
We asked for the additional number of samples of people for the distribution to be accepted as simple and random

We use the formula
np > 10 for random normal distribution

So,
for p = 10%
n (0.10) > 10
n > 100
Therefore, at least 50 more people must be added as samples for the distribution to be simple and random

for p = 15%
n (0.15) > 10
n > 66.67
Therefore, at least 7 more people must be added as samples for the distribution to be simple and random<span />