In a random sample of 300 persons eating lunch at a Lexington pizzeria, 270 ordered pizza. a) Find and interpret a 95% confidence interval for the true proportion of people who eat pizza at this Lexington pizzeria? b) If we take 270/300 = 0.90 as an estimate of the corresponding true proportion, with what confidence can we assert that our error is less than

Ch. 6.1 CI We examine the effect of different inputs on determining the sample size needed to obtain a specific margin of error when finding a confidence interval for a proportion. Find the sample size needed to give, with 95% confidence, a margin of error with +/- 6% when estimating a proportion. Within +/- 4%. Within +/- 1%. (Assume  no prior knowledge about the population proportion p). Comment on the relationship between the sample size and the desired margin of error.

You are interested in constructing a 99% confidence interval for the proportion of all caterpillars that eventually become butterflies. Of the 431 randomly selected caterpillars observed, 50 lived to become butterflies. Round answers to 4 decimal places where possible. a.  With 99% confidence the proportion of all caterpillars that lived to become a butterfly is between___  and___ . b.  If many groups of 431 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.

tion. Use this information to construct the 90% and 95% confidence intervals fc of the confidence intervals. ce of a certain stock was $123.13. Assume the population standard deviation is

Suppose a researcher takes a random sample of 1,000 students from a university and creates a 95% confidence interval for the true proportion of left handed students at the university. Which of the following is true about this interval when compared with a 95% confidence interval based on a random sample of 600 students from the same university? a. The interval based on a sample of 600 students will be wider than the interval based on a sample of 1,000 students. b. The lower and upper endpoints of the 95% CI based on 600 students will both be larger than the corresponding lower and upper endpoints of the 95% CI based on 1,000 students. c. 95% CIs based in samples of 1,000 students are more likely to include the true population proportion than 95% CIs based on samples of 600 students. d. The interval based on a 1,000 students will be wider than the interval based on 600 students.   2. If the researchers above wished to decrease the width of the mean confidence interval for the mean age…

Suppose a new treatment for a certain disease is given to a sample of 190 patients. The treatment was successful for 152 of the patients. Assume that these patients are representative of the population of individuals who have this disease. Calculate a 98% confidence interval for the proportion successfully treated. (Round the answers to three decimal places.) ___ to ___

Section b is where I am struggling