Question

According to the 2000 census, 20.3% of the population of the United States (ages 5 and up) live in a home in which a language other than English is spoken. Advocates for providing government programs to assist non-English speakers are convinced that, with the increasing non-white population in the United States, this proportion has probably increased. They plan to conduct a survey, and if they find the proportion of people who live in such homes has increased, they will organize a campaign to increase government investment in these assistance programs. (i) Write the advocates’ null and alternative hypotheses. (ii) In this context describe a Type I error and the impact such an error would have on this group’s efforts. (iii) In this context describe a Type II error and the impact such an error would have on this group’s efforts. (iv) Based on data that were collected during the survey, the advocate group found that a 99% confidence interval for the proportion of all U.S. residents who live in a home in which a language other than English is spoken (19.8%, 25.2%). What conclusion should they reach about the population? Explain.

Answer 1