Question

We do an email poll of a large community to determine if there is evidence for the claim that the percentage of people in the community living in a mobile home is greater than 10%. We get responses from 100 people. Are the conditions and assumptions met so that we may proceed with a hypothesis test?

Answer 1

Solution:

Given:

p = proportion of people in the community living in a mobile home = 10% = 0.10

n = sample size = 100

We have to check if conditions and assumptions met so that we may proceed with a hypothesis test.

Following are the conditions:

and

and

Thus both the conditions are satisfied.

Since both the conditions are met, thus we can assume large enough sample and thus applying central limit theorem, sampling distribution of sample proportions is approximately Normal with mean of sample proportions is:

and standard deviation of sample proportions is:

Thus the conditions and assumptions are met so that we may proceed with a hypothesis test.