Question

According to a very large poll in 2015, about 90% of homes in California had access to the internet. Market researchers want to test if that proportion is now higher, so they take a random sample of 1,000 homes in California and find that 920—or 92% of homes sampled—have access to the internet. Let p represent the proportion of homes in California that have access to the internet. Which of the following is an appropriate set of hypotheses for their significance test?

a) Null Hypothesis (H0): p ≤ 0.90; Alternative Hypothesis (Ha): p > 0.90
b) Null Hypothesis (H0): p ≥ 0.92; Alternative Hypothesis (Ha): p < 0.92
c) Null Hypothesis (H0): p = 0.92; Alternative Hypothesis (Ha): p ≠ 0.92
d) Null Hypothesis (H0): p < 0.90; Alternative Hypothesis (Ha): p ≥ 0.90

Answer 1

The appropriate hypotheses for a test investigating if the proportion of homes with internet access in California has increased from 90% are Null Hypothesis (H0): p ≤ 0.90 and Alternative Hypothesis (Ha): p > 0.90.

Step-by-step explanation:

When conducting a hypothesis test on the proportion of homes in California with access to the internet, the correct hypotheses should be based on the claim we want to test. Since the market researchers want to test if the proportion is now higher than the previously reported 90%, we're looking at a one-tailed test where the null hypothesis assumes the proportion has not increased and the alternative hypothesis assumes the proportion has increased.

Therefore, the appropriate set of hypotheses for this significance test is:

• Null Hypothesis (H0): p ≤ 0.90
• Alternative Hypothesis (Ha): p > 0.90

This assumes that there has been no change or a decrease in the proportion, versus the alternative which posits that there has been an increase.