A recent survey by the Cable & Telecommunications Association for Marketing found sta-tistical evidence that more than 50% (a majority) of households in the United States have ahigh-definition television (HDTV). A researcher, who doubted this result, decided to repeatthis sampling experiment to see if she could find statistical evidence at the 5% significancelevel that less than 50% of households have an HDTV. This researcher selected 1200 UShouseholds, and found that 564 out of 1200 households had an HDTV.(a) State the null and alternative hypotheses.(b) What assumptions must be made to conduct this hypothesis test?1

(c) Compute the rejection region.(d) Compute the test statistic realization andp-value.(e) State the conclusion to this test.