der a probler stimating the difference of proporti рopulatior sample 1, out of n1 subjects, S1 of them are "successes" and the rest are "failures". In sample 2, out of n2 bjects, S2 of them are "successes" and the rest are "failures". is known that S1 · B(n1,P1) and S2 ~ B(n2, p2). e are interested in estimating pi – P2- Denote îi = 1 and p2 = 2. Show that Pi – P2 is an unbiased estimator for p1 – P2. And what is the mean squared error of it? n2 Explain how CLT would be applied to approximate the distribution of pi – P2 so that pi(1 — р1) , Р2(1 — рә) Pi – P2 ~ N ( Pi – P2, + approximately n1 n2

der a probler stimating the difference of proporti рopulatior sample 1, out of n1 subjects, S1 of them are "successes" and the rest are "failures". In sample 2, out of n2 bjects, S2 of them are "successes" and the rest are "failures". is known that S1 · B(n1,P1) and S2 ~ B(n2, p2). e are interested in estimating pi – P2- Denote îi = 1 and p2 = 2. Show that Pi – P2 is an unbiased estimator for p1 – P2. And what is the mean squared error of it? n2 Explain how CLT would be applied to approximate the distribution of pi – P2 so that pi(1 — р1) , Р2(1 — рә) Pi – P2 ~ N ( Pi – P2, + approximately n1 n2

College Algebra

7th Edition

ISBN:9781305115545

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter9: Counting And Probability

Section9.3: Binomial Probability

Problem 2E: If a binomial experiment has probability p success, then the probability of failure is...

See similar textbooks

Similar questions

Suppose the probability of incorrectly transmitting a single bit is . Compute the probability of correctly receiving a -word coded message made up of -bit words.
If a binomial experiment has probability p success, then the probability of failure is ____________________. The probability of getting exactly r successes in n trials of this experiment is C(_________, _________)p (1p)
Suppose the probability of erroneously transmitting a single digit is P=0.03. Compute the probability of transmitting a 4-bit code word with (a) at most one error, and (b) exactly four errors.
A statistician read that 77% of the population oppose replacing $1 bills with $1 coins. To see ifthis claim is valid, he selected a sample of 80 people and found that 55 were opposed toreplacing the $1 bill. At α = 0.01, test the claim that at least 77% of the population are opposedto change
A real estate office wants to make a survey in a certain town, which has 50,000 households, to determine how far the head of household has to commute to work. A simple random sample of 1,000 households is chosen, the occupants are interviewed, and it is found that on average, the heads of the sample households commuted 8.7 miles to work; the SD of the distances was 9.0 miles. (All distances are one-way; if someone isn't working, the commute distance is defined to be 0.) Fill in the following blanks, rounding to 1 decimal place. And please input part b as lower bound to upper bound. (a) The average commute distance of all 50,000 heads of households in the town is estimated as _______ miles, and this estimate is likely to be off by _________ miles or so. (b) The 95%- confidence interval for the average commute distance of all heads of households in the town is from ________ to ___________ Fill in the blanks
Suppose that a new Internet company Mumble.com requires all employees to take a drug test. Mumble.com can afford only the inexpensive drug test—the onewith a 5% false-positive rate and a 10% false-negativerate. (That means that 5% of those who are not usingdrugs will incorrectly test positive and that 10% of thosewho are actually using drugs will test negative.) Supposethat 10% of those who work for Mumble.com are usingthe drugs for which Mumble is checking. (Hint: It maybe helpful to draw a tree diagram to answer the questionsthat follow.)a. If one employee is chosen at random, what is theprobability that the employee both uses drugs and testspositive?b. If one employee is chosen at random, what is theprobability that the employee does not use drugs buttests positive anyway?c. If one employee is chosen at random, what is the probability that the employee tests positive?d. If we know that a randomly chosen employee has testedpositive, what is the probability that he or she usesdrugs?
The television show Lett3rs has been successful for many years. That show recently had a share of 19, which means, that among the TV sets in use, 19% were tuned to Lett3rs. An advertiser wants to verify that 19% share value by conducting its own survey, and a pilot survey begins with 10 households have TV sets in use at the time of a Lett3rs broadcast. If at most one household is tuned to Lett3rs, does it appear that the 19% share value is wrong? (Hint: Is the occurrence of at most one household tuned to Lett3rs unusual?) A. no, it is not wrongB. yes, it is wrong
There are a total of 27 people in an application pool, that are equally qualified for a job. The pool consists of; 19 females and 8 males There are 4 job openings for 4 different people. Type your answers as a decimal to 4 decimal places. 4. If all 4 people that are hired are female, does your answer to the previous problem indicate that this was due to gender bias in the hiring process?Note: If the probability of randomly hiring only females for the 4 open positions is less than 5%, then we will say that this is so unlikely, that there is gender bias in the hiring process. Yes, this supports a charge of gender dicrimination. There is less than a 1% chance that this could happen by chance Yes, this supports a charge of gender discrimination. There is less than a 5% chance that this could happen by chance No, this does not support a charge of gender discrimination. It is impossible to tell.
3) A medical association claims that less than 20% of adults in the US are regular smokers of tobacco. To test this claim the survey a sample of 125 US adults and find that 19 of them are regular smokers. Test the medical association's claim using α=0.05.