Beth wants to determine a 99 percent confidence interval for the true proportion p of high school students in the area who attend their home basketball games. Out of n randomly selected students she finds that that exactly half attend their home basketball games. About how large would n have to be to get a margin of error less than 0.03 for p?
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- You are interested in constructing a 90% confidence interval for the proportion of all caterpillars that eventually become butterflies. Of the 427 randomly selected caterpillars observed, 45 lived to become butterflies. a. Use 3 decimal places to complete the following statement: With 90% confidence the proportion of all caterpillars that lived to become a butterfly is between and . b. If many groups of 427 randomly selected caterpillars were observed, then a different confidence interval would be produced from each group. About percent of these confidence intervals will contain the true population proportion of caterpillars that become butterflies and about percent will not contain the true population proportion.Suppose you are told that a 95% confidence interval for the average price of a gallon of regular gasoline in your state is from $3.37 to $4.18. Use the fact that the confidence interval for the mean is in the form x − E to x + E to compute the sample mean and the maximal margin of error E. (Round your answers to two decimal places.) x=$ E=$A 95% confidence interval for a population proportion, p, is 0.23 < p < 0.27. What was the sample proportion?
- A sociologist is comparing the proportion of teenage boys who receive a text message at least once an hour to the percentage of teenage girls who do. She has collected data from 150 men and 150 women. Which of the following is not a condition that the sociologist should check before creating a confidence interval for the difference in population proportions?Beth wants to determine a 99% confidence interval for the true proportion of high school students in the area who attend their home basketball games. How large of a sample must she have to get a margin of error less than 0.04? Assume we have no prior estimate of the proportion and want a conservative choice for the sample size. n =A survey of 32,782 adults in 2004 indicated that 24.6% of adults were current smokers. A similar study conducted in 1995 of 40,000 adults indicated that 29.7% were current smokers. a. Find and interpret a point estimate of the difference between the proportion of current smokers in 1995, and the proportion of current smokers in 2004. b. A 95% confidence interval for the true difference is (-0.058,-0.045). Interpret. c. What assumptions must you make for the confidence interval i part b to be valid? (…) a. Find a point estimate of the difference between the proportion of current smokers in 1995 and the proportion of current smokers in 2004. (Round to three decimal places as needed.)
- Suppose that you wanted to know if the percentage of people who will attend a sporting event this year will decrease. Last year, 43% of Americans attended a sporting event. After taking a sample, you attain a sample percentage of 18% with a margin of error of 3%. Construct a confidence interval and use that interval to determine if the number of Americans who will attend a sporting event has decreased. Show your calculation for the interval and then state your conclusion in complete sentences.The Department of Health and Human Services has been asked to estimate the proportion of "latch-key" children (children who have their own key and come home to an empty house) in New Jersey. This estimate is to be within plus or minus 0.03 of the true population proportion with a 98% level of confidence. The head of the Department's Family Division has no idea of what this proportion might be, so she uses 0.5 as the “estimate" of p. What size sample of New Jersey's children should be taken? 5.In a poll, 69% of the people polled answered yes to the question "Are you in favor of the death penalty for a person convicted of murder?" The margin of error in the poll was 2%, and the estimate was made with 96% confidence. At least how many people were surveyed?