Homework Problems due 2/26:

1. A random sample of size 80 is taken from a population of size 600. The sample proportion is 35%.
a. Estimate the population proportion using the expected value.
b. Calculate the the standard error with and without replacement.

Note: Read the first few paragraphs of Page 42 of the class notes that deal with the reliability of the confidence interval.

2. The Residential Energy Consumption Survey found in 2001 that 47% of American households had internet access. A market survey organization repeated this study in a small town with a few thousand households, using a simple random sample of 500 households: 239 of the sample households had internet access.
a. The percentage of households in the town with internal access is estimated as _____; this estimate is likely to be off by _____ or so.
b. If possible, find a 95%-confidence interval for the percentage of households with internet access. If this is not possible, explain.

6. Of the 500 sample households in the previous exercise, 7 had three or more large-screen TVs.
a. The percentage of households in the town with three or more large-screen TVs is estimated as _____; this estimate is likely to be off by _____ or so.
b. If possible, find a 95%-confidence interval for the percentage of households with three or more large-screen TVs. If this is not possible, explain why not.

3. The National Assessment of Educational Progress administers standardized achievement tests to nationwide samples of 17-year-olds in school. One year, the tests covered history and literature. You may assume that a simple random sample of size 6,000 was taken. Only 36.1% of the students in the sample knew that Chaucer wrote The Canterbury Tales, but 95.2% knew that Edison invented the light bulb.
a. If possible, find a 95%-confidence interval for the percentage of all 17-year-olds in school who knew that Chaucer wrote The Canterbury Tales. If this is not possible, why not?
b. If possible, find a 95%-confidence interval for the percentage of all 17-year-olds in school who knew that Edison invented the light bulb. If this is not possible, why not?

4. In an nationwide poll, the proportion of respondents who thought that it should be illegal to use a handheld cellular telephone while driving a car was .69 (69%). Answer the following questions. Round to two decimal places.
a. If the poll's sample size was 1027, find a 95% confidence interval that estimates the population proportion that thinks it should be illegal to use a cellular telephone while driving.
b. If the poll's sample size was 1027, find a 90% confidence interval that estimates the population proportion that thinks it should be illegal to use a cellular telephone while driving.
c. If the poll's sample size was 3052, find a 95% confidence interval that estimates the population proportion that thinks it should be illegal to use a cellular telephone while driving.
d. Compare the widths of the confidence intervals for parts a. and b.
e. Compare the widths of the confidence intervals for parts a. and c.

5. Data from a representative sample were used to estimate that 32% of all computer users in 2011 had tried to get on a WI-Fi network that was not their own in order to save money. You decide to conduct a survey to estimate this proportion for the current year. At a 95% confidence level, what is the required sample size if you want to estimate this proportion with a margin of error of 5%?

Computer Project:

  1. This computer project is to be turned in separately from your daily homework.
  2. Be organized and present things clearly.
You can find the project here.
"Americans: My Member OK, Most in Congress Are Not." by Frank Newport. Gallup, October, 15, 2014.
Document source: Gallup Website.

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