According to Nielsen Company, 21% of households in the United States in 2009 relied solely on their cell phones for phone service instead of landlines. Nielsen also reported that this percentage has steadily increased over the previous years. AT& T recently sampled 125 households randomly to test the hypothesis that the proportion of cell phone– only households increased.

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

b. Using σ = 0.05, calculate the probability of a Type II error occurring if the actual proportion of cell phone– only households is 0.30.

c. Using σ = 0.01, calculate the probability of a Type II error if the actual proportion of cell phone– only households is 0.30.

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