1. A planner wishes to estimate average household size for a community to within an accuracy of ±0.2. The planner desires a 95% confidence level. A small survey indicates that the standard deviation of household size is 2.0. How large should the sample be? 2. A transportation planner wishes to estimate the proportion of commuters who drive to work within 0.05. How large should the sample be, if the planner desires a confidence level of 90%? 3. The tolerable level of a certain pollutant is 16 mg/l. A researcher takes a sample of size n = 50, and finds that the mean level of the pollutant is 18.5 mg/l, with a standard deviation of 7 mg/l. Construct a 95% confidence interval around the sample mean, and determine whether the tolerable level is within this interval. 4. An analyst is interested in knowing whether the proportion of childless couples in a community deviates significantly from the statewide average of 0.12. The analyst suspects a priori that the proportion of childless couples in her community is higher than the statewide average. A sample of 100 couples is interviewed; the mean proportion of childless couples in the sample is found to be 0.16. Test the null hypothesis that the 'true' proportion could be 0.12 and give the p-value. Use a = 0.06. 5. The proportion of people changing residence in the USA each year is 0.165. A researcher believes that the proportion may be different in the town of Amherst. She surveys 50 individuals in the town of Amherst and finds that the proportion who moved last year is 0.24. Is there evidence to conclude that the town has a 90% confidence interval around the sample proportion, and state your conclusion. mobility rate that is different from the national average? Use a = 0.05 and find a 6. A political geographer is interested in the spatial voting pattern during the last presidential election Sho more