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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%? 10.0 comple of

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%? 10.0 comple of

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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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 mobility rate that is different from the national average? Use a = 90% confidence interval around the sample proportion, and state your 6. A political geographer is interested in the spatial voting pattern during the last presidential election. She suspects that university professors in her state were more likely than the statewide population to vote for candidate A. The statewide percentage of the population voting for candidate A was 0.38. She takes a random sample of 45 professors in the state, and finds that 20 voted for candidate A. Is there sufficient evidence to support her hypothesis? Use a = 0.05. What is the p-value? 0.05 and find a conclusion.
Transcribed Image Text: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 mobility rate that is different from the national average? Use a = 90% confidence interval around the sample proportion, and state your 6. A political geographer is interested in the spatial voting pattern during the last presidential election. She suspects that university professors in her state were more likely than the statewide population to vote for candidate A. The statewide percentage of the population voting for candidate A was 0.38. She takes a random sample of 45 professors in the state, and finds that 20 voted for candidate A. Is there sufficient evidence to support her hypothesis? Use a = 0.05. What is the p-value? 0.05 and find a conclusion.
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