Many families have decided to use a satellite dish instead of traditional cable TV. Satellite-dish companies offer a wide variety of premium channels and popular sports packages. The local cable TV provider in Neodesha, Kansas, Cable ONE, is concerned about losing market share and is going to conduct a hypothesis test to determine whether more advertising is needed. A random sample of homes in the city will be obtained, and the data will be used to determine whether there is any evidence that the true proportion of homes with satellite dishes is greater than 0.25.
a. State the null and alternative hypotheses in terms of p.
b. Describe type I and type II errors in this context.
c. For a fixed sample size, which is smaller, b(0.27) or b(0.35)? Justify your answer
South Carolina Department of Natural Resources personnel enforce hunting and fishing regulations and conduct routine safety checks on recreational boats. Past experience indicates that 15% of all boats inspected have at least one safety violation. Recent accidents on lakes in South Carolina have prompted calls for more extensive inspections. A random sample of recreational boats will be obtained and inspected. If there is evidence that the true proportion of boats with safety violations, p, is more than 15%, a methodical inspection of every boat launched at popular sites will be started.
a. State the null and alternative hypotheses in terms of p.
b. Describe a type I error and a type II error in this context.
c. What happens to the probability of a type I error as the value of p approaches 0.15 from the right (that is, 0.20, 0.19, . . .)?