Portland Community College New Green Initiative and Confidence Interval Discussion

A newsgroup is interested in constructing a 99% confidence interval for the proportion of all Americans who are in favor of a new Green initiative. Of the 603 randomly selected Americans surveyed, 415 were in favor of the initiative.

a. With 99% confidence the proportion of all Americans who favor the new Green initiative is between and . Round to 3 decimal places.

b. If many groups of 603 randomly selected Americans were surveyed, then a different confidence interval would be produced from each group. About . percent of these confidence intervals will contain the true population proportion of Americans who favor the Green initiative and about percent will not contain the true population proportion.

A psychologist is interested in constructing a 95% confidence interval for the proportion of people who accept the theory that a person’s spirit is no more than the complicated network of neurons in the brain. 51 of the 812 randomly selected people who were surveyed agreed with this theory.

a. With 95% confidence the proportion of all people who accept the theory that a person’s spirit is no more than the complicated network of neurons in the brain is betweenand . Round to 3 decimal places.

b. If many groups of 812 randomly selected people are surveyed, then a different confidence interval would be produced from each group. About percent of these confidence intervals will contain the true population proportion of all people who accept the theory that a person’s spirit is no more than the complicated network of neurons in the brain and about percent will not contain the true population proportion.

Out of 500 people sampled, 200 had kids. Assuming the conditions are met, construct a 99% confidence interval for the true population proportion of people with kids.

Give your answers as decimals, to three places

If n = 480 and $\stackrel{ˆp}{p}$

Give your answers to three decimals

If n=310 and $\stackrel{ˆp}{p}$

Give your answers to three decimals.

If $\mathrm{n=550}$

In a recent poll, 190 people were asked if they liked dogs, and 31% said they did. Find the margin of error of this poll, at the 99% confidence level.

Give your answer to three decimals

6.18 Is college worth it? Part II: Exercise 6.16 presents the results of a poll where 48% of 331 Americans who decide to not go to college do so because they cannot afford it.

(a) Calculate a 90% confidence interval for the proportion of Americans who decide to not go to college because they cannot afford it, and interpret the interval in context.
lower bound: (please round to four decimal places)
upper bound: (please round to four decimal places) Interpret the confidence interval in context:

• We can be 90% confident that the proportion of Americans who choose not to go to college because they cannot afford it is contained within our confidence interval
• 90% of Americans choose not to go to college because they cannot afford it
• We can be 90% confident that our confidence interval contains the sample proportion of Americans who choose not to go to college because they cannot afford it

(b) Suppose we wanted the margin of error for the 90% confidence level to be about 1.5%. How large of a survey would you recommend?
A survey should include at least

people.

You want to obtain a sample to estimate a population proportion. At this point in time, you have no reasonable estimate for the population proportion, so we assume p=.5. You would like to be 90% confident that you esimate is within 0.2% of the true population proportion. How large of a sample size is required?

You want to obtain a sample to estimate a population proportion. Based on previous evidence, you believe the population proportion is approximately 27%. You would like to be 98% confident that your estimate is within 4.5% of the true population proportion. How large of a sample size is required?

A political candidate has asked you to conduct a poll to determine what percentage of people support her, assume p=.5.
If the candidate only wants a 10% margin of error at a 95% confidence level, what size of sample is needed?