8. An entrant firm may make a technological discovery giving them a product that places strongcompetition on some rival firm who is already in the marketplace. If they don't make such a discovery,then the only product that the entrant could potentially bring to market is a weak product. Naturedetermines whether or not the entrant is "strong" or "weak." The entrant knows its own type, and astrong entrant is 80% likely to challenge the incumbent firm, while a weak entrant is only 65% likely tochallenge the incumbent. There is a 3/4 chance the entrant is strong.a) Compute prob(challenge). That is, compute the unconditional probability that the entrant challenges.b) Compute prob(don't challenge weak). That is, compute the probability that the entrant doesn'tchallenge, conditional on the entrant being weak.c) Is the event "the entrant challenges" statistically independent from the event "the entrant is strong?"Explain why or why not.

The conditional probability, PA|B, is the probability of an event A provided the event B has already…

Answered: 8. An entrant firm may make a…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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06:23 A myopenmath.com You are conducting a study to see if the proportion of voters who prefer the Democratic candidate is significantly smaller than 73% at a level of significance of a = 0.01. According to your sample, 40 out of 59 potential voters prefer the Democratic candidate. a. For this study, we should use Select an answer b. The null and alternative hypotheses would be: Ho: ? O Select an answer > (please enter a decimal) H1: ? 0 Select an answer © (Please enter a decimal) c. The test statistic ? O (please show your answer to 3 decimal places.) d. The p-value (Please show your %3D answer to 4 decimal places.) e. The p-value is ? 0 f. Based on this, we should Select an answer the null hypothesis. g. Thus, the final conclusion is that ... O The data suggest the population proportion is not significantly smaller than 73% at a = 0.01, so there is sufficient evidence to conclude that the proportion of voters who prefer the Democratic candidate is equal to 73%. The data suggest the…
Currently, studies are being done on whether one COVID vaccine (like Pfizer’s) can be mixed and matched with another COVID vaccine (like Moderna’s). So a person could have the first shot of one and the second shot of the other. Let’s say a study was done to try to determine if mixing and matching is as effective as just using one type for both shots. People show up at a clinic on a Saturday (self-selecting), and are first given the Pfizer vaccine, and then the Moderna vaccine 3 weeks later. Suppose the results showed that only 1% of all of the people got COVID. What is a problem with this study? A) There was no random assignment of participants to groups. B) It is observational, and an experiment would have been better due to the potential of confounding. C) There was no control group, i.e. a group to compare the results to. D) All of the above
A poll released this week found that in a random sample of registered voters, 60% indicated that they think a fenmale "will run" for the presidency, 30% said a female “will not run," and 10% had “no opinion." When asked their opinions on whether or not a female could be elected, 66% of those who said a female "will run" thought a female could be elected; 25% of those who thought a female "will not run" thought a female could be elected; whereas, 20% of those who had no opinion said 4. that a female could be elected. а. [2] What percentage of registered voters (in this sample) thought that a female could be elected? [2] Given that a person thought that a female could be elected, what is the probability that this person said a female "will not run" for the presidency? b. [3] Given that a person thought that a female could be elected, which is more likely: that this person said a female “will not run" for the presidency or that this person said a female “will run" for the presidency? C.
7. A sociological study consists of recording the marital status, religion, race, and income of an individual. If marital status is classified into one of four categories, religion into one of three categories, race into one of five categories, and income into one of five categories, how many outcomes are possible for the experiment of recording the information of one of these individuals?
1) The PGA (Professional Golfers Association) performed a survey of 1,000 golf fans. 30% play once per month, 40% play once per week, and 30% play more than once per week. Agolfer who plays once per week is four times more likely than a golfer who plays once per month to have scored below par in a round in the past year, but half as likely as one who plays more than once per week. A randomly selected golfer from the survey has scored below par in a round in the last year. What is the probability that this golfer plays once per month?
1. A machine can be in one of four states: 'running smoothly' (state 1), 'running but needs adjustment' (state 2), 'temporarily broken' (state 3), and 'destroyed' (state 4). Each morning the state of the machine is recorded. Suppose that the state of the machine tomorrow morning depends only on the state of the machine this morning subject to the following rules. • If the machine is running smoothly, there is 1% chance that by the next morning it will have exploded (this will destroy the machine), there is also a 9% chance that some part of the machine will break leading to it being temporarily broken. If neither of these things happen then the next morning there is an equal probability of it running smoothly or running but needing adjustment. • If the machine is temporarily broken in the morning then an engineer will attempt to repair the machine that day, there is an equal chance that they succeed and the machine is running smoothly by the next day or they fail and cause the machine…
4. To determine whether dogs prefer a specific brand of dog food to that of a competitor, market researchers are working with a local dog shelter to randomly select dogs for participation in a study. All randomly selected dogs are put into a large room with two bowls of food — one with their brand and another with the competitor's brand. The first two dogs immediately go for the dog food containing their ingredient, so the researchers stop the experiment, concluding this is enough evidence that their product will sell the most. Is this a good experiment and conclusion? State reasons for your explanation, and what you would do differently?
1. A machine can be in one of four states: 'running smoothly' (state 1), 'running but needs adjustment' (state 2), 'temporarily broken' (state 3), and 'destroyed' (state 4). Each morning the state of the machine is recorded. Suppose that the state of the machine tomorrow morning depends only on the state of the machine this morning subject to the following rules. • If the machine is running smoothly, there is 1% chance that by the next morning it will have exploded (this will destroy the machine), there is also a 9% chance that some part of the machine will break leading to it being temporarily broken. If neither of these things happen then the next morning there is an equal probability of it running smoothly or running but needing adjustment. • If the machine is temporarily broken in the morning then an engineer will attempt to repair the machine that day, there is an equal chance that they succeed and the machine is running smoothly by the next day or they fail and cause the machine…
3.) In a particular epidemic disease, 400 individuals were surveyed by a well-established pharmaceutical company to determine if the company’s new vaccine was effective after 4 months. Among the 120 individuals who had that disease and were given the shot, 29 were cured and achieved immunity after 4 months. Among 280 individuals who had the disease but were not given the shot, 56 were cured and achieved immunity after 4 months. Is there enough statistical evidence to support the company’s claim of the effectiveness of the vaccine?
25. An egg company is studying the effects of artificial lighting on egg production of chickens. A brood of chicks were separated at random into two groups, both raised in windowless coops with artificial lighting. One group followed a natural 24-hour per day light/dark cycle while the second group experienced an accelerated 20- hour day. The weekly egg productions for the two groups are summarized in the table below. Conduct a hypothesis test to determine whether egg production is higher with a 20-hour day as compared to a 24-hour day. The level of significance is 1%. Wnat is the conclusion of the hypothesis test? Sample size Mean number of eggs Standard Deviation 24-hour day (Group 2) 20-hour day (Group 1) 45 5.2 1.8 42 6.1 2.9 A. We have enough evidence to conclude that the sample mean egg production with artificial lighting at a 20-hour day is higher than that at a 24-hour day. B. We do NOT have enough evidence to conclude that the sample mean egg production with artificial…
5. Two processes A and B, were used to produce stainless steel shafts in an industrial company. Process A and Process B produce 9% and 12% nonconforming stainless steel shafts, respectively. a. A random sample of 100 stainless steel shafts were taken from Process A. What is the UTM probability that more than 95% of the stainless steel shafts are conforming? b. A random sample of 90 stainless steel shafts from Process A and 80 stainless steel shafts UTM UT UTM 8U from Process B were taken randomly. Find the probability that the difference between proportion of the nonconforming stainless steel shafts from Process A and Process B UTM UTM is at most 0.1. O UTM UT UTM 6 UTM U O UTM UT

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