According to Pew Research, 21% of people who use online dating services are 35 to 44 years old. There is also information that this percentage has steadily increased over the previous years. Assume Pew recently sampled 125 households randomly to test the hypothesis that the proportion of people aged 35 to 44 who use online dating services has increased.

a. Explain in your own words how Type I and Type II errors can occur in this hypothesis test.

b. Using α = 0.05, calculate the probability of a Type II error occurring if the actual proportion of people who use online dating services between 35 and 44 is 0.30.

c. Using α = 0.01, calculate the probability of a Type II error if the actual proportion of people who use online dating services between 35 and 44 is 0.30.

d. Explain the differences in the results you calculated in parts b and c.