# Question: You are told that a ball will be randomly drawn

You are told that a ball will be randomly drawn from one of two boxes (A and B), both of which contain black balls and red balls, and if a red ball is chosen, you will win $100. You are also told that Box A contains half black balls and half red balls, but you are not told the proportions in Box B. Which box would you pick?

a. Set up notation and specify hypotheses to test whether the population proportion who would pick Box A is 0.50.

b. For a random sample of 40 people, 36 pick Box A. Can you make a conclusion about whether the proportion for one option is higher in the population? Explain all steps of your reasoning. (Logically those who picked Box A would seem to think that Box B has greater chance of a black ball. However, a paradox first discussed by Daniel Ellsberg predicts that if they were now told that they would instead receive $100 if a black ball is chosen, they would overwhelmingly pick Box A again, because they prefer definite information over ambiguity.)

a. Set up notation and specify hypotheses to test whether the population proportion who would pick Box A is 0.50.

b. For a random sample of 40 people, 36 pick Box A. Can you make a conclusion about whether the proportion for one option is higher in the population? Explain all steps of your reasoning. (Logically those who picked Box A would seem to think that Box B has greater chance of a black ball. However, a paradox first discussed by Daniel Ellsberg predicts that if they were now told that they would instead receive $100 if a black ball is chosen, they would overwhelmingly pick Box A again, because they prefer definite information over ambiguity.)

## Answer to relevant Questions

A fraternity at a university lobbies the administration to start a hockey team. To bolster its case, it reports that of a simple random sample of 100 students, 83% support starting the team. Upon further investigation, their ...For a quantitative variable, you want to test H0: μ = 0 against Ha: μ ≠ 0. The 10 observations are 3, 7, 3, 3, 0, 8, 1, 12, 5, 8. a. Show that (i) x = 5.0, (ii) s = 3.71, (iii) Standard error = 1.17, (iv) Test statistic ...Management claims that the mean income for all senior-level assembly-line workers in a large company equals $500 per week. An employee decides to test this claim, believing that it is actually less than $500. For a random ...Refer to the FL Student Survey data file on the text CD. Test whether the (a) Population mean political ideology (on a scale of 1 to 7, where 4 = moderate) equals or differs from 4.0. (b) Population proportion favoring ...As part of her class project in a statistics course, a student decided to study ways in which her fellow students use the Internet. She randomly sampled 5 of the 165 students in her course and asked them, “In the past ...Post your question