Question

According to a very large poll in 2015, about 90% of homes in California had access to the internet. Market researchers wonder if that proportion is now higher, so they take a random sample of 200 homes in California and find that 196 have access to the internet. They want to use this sample data to test Hop = 0.9 versus Hap > 0.9, where p is the proportion of California homes with internet access.

Which conditions for performing this type of significance test have been met?
Choose all answers that apply.
I. The data is a random sample from the population of interest.
II. np ≥ 10 and n (1-p) ≥ 10
III. Individual observations can be considered independent.
O I only
O I, II, and III
O I and III
O I and II
O II and III
O III only
O II only

Answer 1

All conditions I, II, and III have been met for performing the significance test on the proportion of homes in California with internet access: the data is a random sample, the np and n(1-p) conditions are satisfied, and the observations can be considered independent.

Step-by-step explanation:

The conditions for performing a significance test on the proportion of homes in California with internet access are as follows:

1. I. The data is a random sample from the population of interest. This condition appears to have been met as the question implies that a random sample of 200 homes was selected.
2. II. np ≥ 10 and n(1-p) ≥ 10. With n=200 and p=0.9, np=180 and n(1-p)=20, both of which are greater than 10, so this condition is met.
3. III. Individual observations can be considered independent. Since the sample size is less than 10% of the population, we can assume independence.

Therefore, all conditions I, II, and III have been met for performing the significance test.