Answered: an automobile engineer claims that 1in…

an automobile engineer claims that 1in 10 automobile accidents are due to driver fatigue . if a random sample of 5 accidents observed , then the probabilty that 3 accidentsare due to drive fatigue is

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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Before the semester began, Professor Keithley predicted that 15% of hisphilosophy students would receive an A, 30% a B, 40% a C, 10% a D, and 5%an F. At the end of the semester, 14 of Professor Keithley’s philosophy studentsearned an A, 19 a B, 12 a C, 5 a D, and 2 an F.Use the Chi-Square test and a 0.05 level of significance to determine if ProfessorKeithley’s predicted percentages were accurate. (State your null and alternativehypothesis, find the critical values and test statistics, make a decision, and writea conclusion based on your results).
Following an oil spill, a particular region of the ocean is being tested for the level of a chemical called naphthalene. It is considered fact that fish from the region will be safe to eat if, and only if, the mean naphthalene level in the region is less than 3.3 parts per billion. A set of water specimens will be randomly selected from the region and tested, and if the results provide convinving evidence that the mean naphthalene level is less than 3.3, then the sale of fish from the region will be made legal. Which of the following describes a Type I error and its consequences? A) the authorities fail to obtain convincing evidence that the mean naphthalene level is less than 3.3, and do not legalize the sale of fish from the region when in fact the fish are SAFE for consumption. B) The definition of a Type I error depends on the actual results of the study in question C) The authorities fail to obtain convincing evidence that the mean naphthalene level is less than 3.3, and do not…
A state policeman has a pet theory that people who drive red cars are more likely to drive too fast. Onhis day off, he borrows one of the department’s radar guns, parks his car in a rest area, and measures theproportion of red cars that are driving too fast. (He decides ahead of time to define “driving too fast” asexceeding the speed limit by more than 5 miles per hour.) To produce a random sample, he rolls a dieand only includes a car in his sample if he rolls a 5 or a 6. He finds that 18 of 28 red cars are driving toofast, and 75 of 205 other cars are driving too fast. please run a 4 step process(significance test) and interperet the P-value for ap stats
Suppose you are a quality assurance manager for Honda. A new model of family car has been built, and the engineers are interested in testing the new model to ensure it meets Canadian safety standards. The safety standards indicate that the vehicle must be able to stop within 17.38 metres from a speed of 48.3 km/h [1]. Note this means the quality assurance team wants to ensure the cars stop in less than 17.38 metres on average). They obtain a random sample of 21 new model cars, and test the brakes on each car. The sample mean stopping distance from this sample of 21 cars is 17 metres. Suppose the population standard deviation is 1.25 metres. Conduct an appropriate hypothesis test using the critical value method. Based on your answer to part a.,do you believe the company can sell the new model car in Canada? Why or why not?
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The National Academy of Science reported that 33% of research in mathematics is published by US authors. The mathematics chairperson of a prestigious university wishes to test the claim that this percentage is no longer 33%. He has no indication of whether the percentage has increased or decreased since that time. He surveys a simple random sample of 280 recent articles published by reputable mathematics research journals and finds that 108 of these articles have US authors. Does this evidence support the mathematics chairperson’s claim that the percentage is no longer 33%? Use a 0.01 level of significance. Step 1 of 3 : State the null and alternative hypotheses for the test. Fill in the blank below. H0: p = 0.33 Ha: p___ 0.33
One cable company claims that it has excellent customer service. In fact, the company advertises that a technician will arrive within 55 minutes after a service call is placed. One frustrated customer believes this is not accurate, claiming that it takes over 55 minutes for the cable technician to arrive. The customer asks a simple random sample of 4 other cable customers how long it has taken for the cable technician to arrive when they have called for one. The sample mean for this group is 62.1 minutes with a standard deviation of 8.3 minutes. Assume that the population distribution is approximately normal. Test the customer’s claim at the 0.05 level of significance. Step 2 of 3 : Compute the value of the test statistic. Round your answer to three decimal places.
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A set of data was published in the fall 2019 Phi Kappa Phi Forum regarding the performance of Major League Baseball (MLB) umpires in calling balls and strikes. The article is based on data collected by MLB over eleven seasons (2008-2018). This study shows that it is common for umpires to make incorrect calls more than 20% of the time. An average game has about 300 pitches where the umpire has to make a decision. Assume that we take a random sample of 300 of the 4 million ball/strike calls in the database. Our analysis of a new sample yielded a Z test statistic of 2.17 for this one-sided test to the right. The p-value is = .015. Make a decision on this hypothesis test using a 5% level of significance and state the reason for your decision. O Reject the null hypothesis since the p-value is .01
Some people claim that they can tell the difference between a diet soda and a regular soda in the first sip. A researcher wanting to test this claim randomly sampled 80 such people. He then filled 80 plain white cups with soda, half diet and half regular through random assignment, and asked each person to take one sip from their cup and identify the soda as diet or regular. 53 participants correctly identified the soda. 1. Do these data provide strong evidence that these people are able to detect the difference between diet and regular soda, in other words, are the results significantly better than just random guessing? 2. Interpret the p-value in this context.
The National Academy of Science reported that 41% of research in mathematics is published by US authors. The mathematics chairperson of a prestigious university wishes to test the claim that this percentage is no longer 41%. He has no indication of whether the percentage has increased or decreased since that time. He surveys a simple random sample of 186 recent articles published by reputable mathematics research journals and finds that 92 of these articles have US authors. Does this evidence support the mathematics chairperson’s claim that the percentage is no longer 41%? Use a 0.05 level of significance. Step 1 of 3: State the null and alternative hypotheses for the test. circle the answer below. H0 p=0.41 ha: p⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯0.41 A.<B.≠C.> Step 2 of 3: Compute the value of the test statistic. Round your answer to two decimal places Step 3 of 3: Draw a conclusion and interpret the decision. A. We reject the null hypothesis and conclude that there is insufficient evidence at a…