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- Suppose we want to estimate the proportion of the Helena population who have used marijuana within the last month. We select 4328 participants and ask them each to first privately draw a card from a standard 52-card deck. If they get a “club” they are asked to respond truthfully to the question “Have you used marijuana within the last month?”If they get any other suit they are asked to respond to the question “Does your phone number end in an odd digit?”The study is blinded in the sense that the researcher doesn’t know which question the participant is answering. Hence, participants are guaranteed anonymity and are more likely to be truthful in their responses. The researchers only get a “yes” or “no” answer from each respondent and don’t know the actual results of the card draw. What is the expected probability of a person’s phone number ending in an odd digit? What is the expected probability of a person’s phone number not ending in an odd digit?6) A small business owner you follow on TikTok is SO EXCITED because last month, she was able to begin selling her product in a popular chain store around the nation. Her contract with the chain store says that at any time, there will be at least 20 of her products sitting out on the shelves. She wants to conduct a survey to see if that is true. She visits 5 of the local chain stores around her and records the number of products of hers that are on the shelves. She will then construct a 95% confidence interval to determine the mean number of products on the shelves for all of the stores. (a) Discuss whether this study meets the each of the conditions for constructing a confidence interval. If one of the conditions has not been met, what additional information would be required or what change in the study would you recommend? (b) If, instead of constructing a 95% confidence interval, the business owner constructed a 98% confidence interval, would the 98% interval be wider, narrower, or…9. A group of 50 single men were asked which dating apps they had on their phones. The follo data were collected: 33 of the men had the Tinder app. 30 of the men had the Coffee Meets Bagel app. 26 of the men had the Hinge app. 16 of the men had both the Tinder and Coffee Meets Bagel apps. 14 of the men had both Tinder and Hinge apps. 18 men had both Hinge and Coffee Meets Bagel apps. 7 men had all three apps on their phones. a) Represent this information in a Venn diagram: b) Calculate the number of single men who have none of these apps on their phone. c) How many single men only had Tinder on their phone? d) How many students own at most two of the apps?
- 1. An experiment consists of flipping a coin until either heads is flipped 6 times, or the same side shows up 3 times in a row. The random variable X assigns the number of total coins flips to each outcome. What number is assigned to HTTT? 2. A person picks a number between 1 and 28536. The random variable Z assigns the number picked to each outcome. What number is assigned to 267927? 3. A person picks a number between 1 and 285336. The random variable Z assigns the 0 to an even number 1 to an odd number. What number is assigned to 267927?8. A student runs an experiment to test how microwave power and temperature affect popping. Each bag of popcorn can be popped for 3 minutes or 4 minutes. The microwave power can be set to low, medium and high. Each combination of time and power is tested on one bag of popcorn and the number of unpopped kernels is recorded. The number of treatments in this experiment are: • 12 • 6 • 4Please provide a neat solution thank you!
- 2.4.4 A bag contains 1 red, 1 black and 1 green marble. I randomly select 1 of the marbles and record its color. I then replace it in the bag, shake the bag, and randomly select a second marble, again recording its color. The second marble is then replaced and a third marble is randomly selected and its color recorded. How many different samples of 3 colors could occur?To study the security protocols at a major airport, ten passengers were randomly selected from each flight leaving the airport on a particular day and questioned about the security efforts they experienced while at the airport. This is an example of250 adults are practicing every day before taking part in a high-stakes children's game. The game requires them carefully to remove a shape- either a star or an umbrella-from a sugar wafer. 30% of those who choose stars on a given day will switch to umbrellas the next day, and 20% of those who choose umbrellas on a given day will switch to stars the next day. (a) If 150 contestants practice with stars today, how many will practice with umbrellas tomorrow? (b) If the actual game is held a long time from now, what proportion of contestants do we expect will be practicing with stars each day close to then?
- 8. A set of 5 coins is tossed 3200 times and the number of heads appearing each time įs noted. The results are given below : 4 5 No. of Heads 2 900 500 50 Frequency 80 570 1100 Test the hypothesis that the coins are unbiased.The school district sets up two locations to help students with technical difficulties over the summer. They believe the technicians they have assigned to location 2 are being lazy and not helping students as much as they should be so they take a random sample of 15 students from each of the two locations and ask if their technical issue had been resolved (over 200 students had asked for assistance at each location). Twelve of the 15 students from location 1 reported their technical issue had been resolved and 8 of the 15 students from location 2 reported their technical issue had been resolved. Is this convincing evidence that the technicians from location 2 are being lazy and not helping students as much as those from location 1?Bowl A contains 2 red chips; bowl B contains two white chips; and bowl C contains 1 red chip and 1 white chip. A bowl is selected at random, and one chip is taken at random from that bowl.
