A research firm supports a consumer panel of 2000 households that keep written diaries of their weekly grocery expenditures. The firm would like to estimate, with 95% confidence and within 4 percentage points, the percentage of its panel households who would be interested in providing more extensive information in return for an extra $50 per week remuneration.
How many of the households should be surveyed? Explain any assumptions you used in obtaining your recommended sample size.