When the Euro coin was introduced in 2002, two math professors had their statistics students test whether the Belgian one Euro coinwas a fair coin. They spun the coin rather than tossing it and found that out of 250 spins, 160 showed a head (event H) while 90showed a tail (event T). On that basis, they claimed that it is not a fair coin.O Part (a)Based on the given data, find P(H) and P(T). (Round your answers to two decimal places.)P(H) = 0.6P(T) = 0.4O Part (b)Use a tree diagram to find the probabilities of each possible outcome for the experiment of spinning the coin twice. (Round your answers to fourdecimal places.)HH, 0.6400TTTH, 0,2304HTO Part (c)Use the tree diagram to find the probability of obtaining exactly one head in two spins of the coin. (Round your answer to four decimal places.)O Part (d)Use the tree diagram to find the probability of obtaining at least one head. (Round your answer to four decimal places.)Additional MaterialsO Reading

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MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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3. Bayesian Inference A cab was involved at night in a hit and run accident. In this town there are only two cab companies, the Blue with 80% of the cabs and the Green company with the remaining 20%. As it happened there was a witness to the accident who identified the hit and run cab as Blue. The case came to trial. An important part of the testimony was a test of the reliability of the eyewitness to identify a cab as being either Blue or Green under the same circumstances as those that existed the night of the accident. The result of these tests was that the witness correctly identified a blue cab as blue 70% of the time and a green cab as green 80% of the time. On the basis of the claim of the eyewitness and the test conducted by the court, what is the probability that the cab involved in the accident was in fact Blue as the witness had claimed?
Sleep researchers were trying to understand the impact of cell phone use before bedtime on the amount of time it took a person to fall asleep. Using a matched pairs design, they chose 8 subjects and recorded the amount of time it took the subject to fall asleep, both when using the cell phone up to attempting to sleep and stopping using the cell phone 2 hours prior to attempting to sleep, in random order. The amount of time for each person for each attempt is recorded in the table below. Person 1 2 3 4 5 6 7 8Until Attempt 22 17 45 15 35 19 36 18Two Hours Prior 18 18 40 8 23 15 32 12Difference a. Compute the difference for each observation.b. Based on the above data compute the mean and sample standard deviation of the difference.
The two-way table below shows teenage driver gender and whether or not the respondent had texted at least once while driving during the last thirty days. Teenage driver- Teenage driver- Male Female Texted at least once while driving during past 30 days. Had not texted at least once while 7 11 9 driving during the past 30 days. What percentage of the sample had texted at least once while driving in the past thirty days? O 37.5% O 62.5% De O 50% O 43.75%
You find a coin in the street and are flipping it while walking away. You happen to look at the outcomes of your coin flips and notice heads is showing up more than you think it should. After 10 flips, the coin has landed on heads 8 of the 10 flips. Deciding you need more data, you flip the coin 25 more times and it lands heads up 18 times. You have now flipped the coin 35 times, 26 of which have landed heads. You are still surprised of these results, so you decide to flip the coin 100 more times and record the data. This time, the coin landed heads up 75 times. Now, you flip your coin 135 times, and it lands heads up 101 times. Are you convinced that the coin you have found is weighted, meaning that it favors one outcome over the other? Why? What is the name of the property of probability shown in the previous example? (continuous probability, discrete probability, law of averages, law of large numbers)
Ecologists conducted a study to investigate the potential ecological impact of golf courses. Investigators monitored the reproductive success of bluebirds in birdhouses at nine golf courses and ten similar birdhouses at nongolf sites. Data on nests in birdhouses occupied only by bluebirds are shown in the table. If the proportions of nests occupied is the same for golf and nongolf sites, what would be the expected count of birdhouse with 1 nest in nongolf locations? O nests 1 nest Total 2 or 3 nests Golf 30 42 8 80 Nongolf 40 58 22 120 Total 70 100 30 200 50 b 42 60 d. 58 e 40 O O O O O
How many different ways are there to select a group of 4 out of 8 people for a survey?
Researchers wish to study the effect of daily brain teasers on a person's intelligence. The researchers randomly choose 20 students from their local college campus. Day one of the test, every student is given an IQ test. The students are then randomly divided into Group A and Group B (10 students each). Group A is given daily brain teasers, while Group B were not instructed to participate in anything outside their normal routine. At the end of a 30 day period, each member of the group takes an IQ test. The students are aware of what group they are in, but the researchers have no idea until the results are given. The test given to Group A would be considered the Control Treatment Variable Placebo
An employee at the metropolitan museum of art surveyed a random sample of 150 visitors to the museum of those visitors 45 people bought food at the cafeteria based on those results how many people out of 1750 visitors to the museum would be expected to buy food from the cafeteria?
2. In a population it is estimated that 20% have a desired trait of interest for the researcher. The researcher wants to know how many people on average he has to draw from a population to get 2 people with the trait. Use rows 20-24 of the Random Number Table to carry out the simulation. Explain clearly how you set up the problem and report your findings. Answer:
Q3 i): A survey of 500 randomly chosenindividualsis conducted. The individuals are askedto nametheir faxorite sport. The STATISTIX pie chart inthe following figure summarizesthe results of this survey Other (5.0%)- Hockey (10.0%)- -Baseball (30.0%) Golf (10.0%)- Footbal (25.0%)- -Basketbal (20.0%) Fig. 2-11 STATISTIX pie chart La) How many individuals inthe 500 gave baseball astheirfavorite sport? (b) How mary gave a sport other than basketball as their favorite sport? L) How many gave hockey or golf astheir favorite sport? ii) Thefollowing table gives the frequency distribution for the cholesterol values of 45 patients ina cardiacrehabilitation study. Givethe IgweLandupper class limits and boundaries as well asthe class marks for each class Chalastarol vala Fraquancy 170 to 189 190 to 209 10 210 to 229 17 230 to 249 13 250 to 269
Suppose that you roll several ordinary six-sided dice, choose two of those dice at random, and average the two numbers. Suppose the average of these two dice is 3.5. How would you express the 3.5 in statistical notation?
A high school track coach wanted to test whether giving the students an energy drink could affect performance during the 100 meter race. The coach split the 26 boys into two equal sized groups, where Group 1 was given the energy drink and Group 2 was not. The 100 meter race times were recorded during practice and shown in the table below. What inference can be made about the results? Group 1 Group 2 12.2 13 12.5 12.3 13.3 12.8 12.9 13 13 13.8 12.1 13 13 13 13 13 12.1 13 13 13 12.1 13 12.8 13 13 12.6 Mean: 12.7 Mean: 13 Since the simulation shows ( many cases or free cases )? where a mean difference of ( solve for this answer ) or less occurred when the groups were re-randomized, it can be inferred that the mean difference observed in the study was ( very possibly or very unlikely ) ?due to the random assignment of participants into groups, so the results of the study are (…

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