1.12 It was noted in Section 1.2.1 that statisticians who follow the deFinetti school do notaccept the Axiom of Countable Additivity, instead adhering to the Axiom of FiniteAdditivity.(a) Show that the Axiom of Countable Additivity implies Finite Additivity.(b) Although, by itself, the Axiom of Finite Additivity does not imply CountableAdditivity, suppose we supplement it with the following. Let A₁ A₂ 3An D... be an infinite sequence of nested sets whose limit is the empty set, whichwe denote by An 10. Consider the following:Axiom of Continuity: If An 10, then P(An) → 0.Prove that the Axiom of Continuity and the Axiom of Finite Additivity implyCountable Additivity...

Given the statements:i. The Axiom of Countable Additivity implies Finite Additivityii. The Axiom of…

Answered: 1.12 It was noted in Section 1.2.1 that…

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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It is suspected that the higher-priced automobiles are assembled with greater care than lower- priced automobiles. To investigate whether there is any basis for this feeling, a large luxury model A, a medium-size sedan B, and a subcompact hatchback C were compared for defects when they arrived at the dealer's showroom. All cars were manufactured by the same company. The number of defects for several of the three models are recorded below. Number of Automobile Defects Model A В 4 8 7 1 6. 6. 8 5 9. 3 4 Total 23 21 36 80 Test the hypothesis at the 0.05 level of significance that the average number of defects is the same for the three models.
Suppose a business person wishes to open a store in a local shopping centre only if there is strong evidence that the average number of people in the centre is greater than 5000 per day. What is the null hypothesis will be: H0: μ < 5000 or H0: μ > 5000 or H0: μ ≤ 5000 or H0: μ ≥ 5000
A research center claims that at least 31% of adults in a certain country think that their taxes will be audited. In a random sample of 900 adults in that country in a recent year, 26% say they are concerned that their taxes will be audited. At a= 0.05, is there enough evidence to reject the center's claim? Complete parts (a) through (e) below. (a) Identify the claim and state Ho and H. Identify the claim in this scenario. Select the correct choice below and fill in the answer box to complete your choice. (Type an integer or a decimal. Do not round.) O A. Less than % of adults in the country think that their taxes will be audited. O B. % of adults in the country think that their taxes will be audited. O C. At least 31 % of adults in the country think that their taxes will be audited. O D. The percentage of adults in the country who think that their taxes will be audited is not Let p be the population proportion of successes, where a success is an adult in the country who thinks that…
3 4. 8 10 11 12) 13) K 12 Question 12 For a certain brand of tomato seeds, the seed package claims that it takes 87 days after planting for the tomato plants to produce fruit. Sarah, a botanist, wanted to know whether the mean number of days for the plants to produce fruit where she lives is different from 87 days. She planted 40 seeds and recorded the number of days for each plant to produce fruit. With all conditions for inference met, the hypothesis test was conducted at the significance level a = 0.05, and the test resulted in a pvalue of 0.0752. Which of the following is a correct conclusion? A Sarah has convincing statistical evidence to conclude that the population mean number of days for the plants to produce fruit is greater than 87 days. B Sarah has convincing statistical evidence to conclude that the population mean number of days for the plants to produce fruit is different from 87 days. Sarah does not have convincing statistical evidence to conclude that the population…
You wish to test the following claim (Ha) at a significance level of a = 0.005. Ho: P1 = P2 Ha: P₁ P2 You obtain 586 successes in a sample of size n₁ = 685 from the first population. You obtain 504 successes in a sample of size n2 = 541 from the second population. What is the test statistic for this sample? (Report answer accurate to three decimal places.) test statistic = What is the p-value for this sample? (Report answer accurate to four decimal places.) p-value = The p-value is... O less than (or equal to) a Ogreater than a This test statistic leads to a decision to... O reject the null O accept the null O fail to reject the null
You are conducting a multinomial hypothesis test (a = 0.05) for the claim that all 5 categories are equally likely to be selected. Complete the table. Observed Expected Frequency Category Frequency A 13 В 21 15 11 E 19 (a) Determine the null and alternative hypotheses. 1 O Ho: PA = PB = Pc = Pp = Pe %3D %3D 5 Ha: At least one proportion is different O Ho: PA = PB = Pc = Pp = PE Ha: At least one proportion is different O Ho:The catagories are independent Ha: The categories are dependent (b) What is the chi-square test-statistic for this data? (Report answer accurate to three decimal places) (c) What are the degrees of freedom for this test? d.f.= (d) What is the p-value for this sample? (Report answer accurate to four decimal places.) p-value = (e) Is the p-value less than a? O yes O no
SI jinx Players in any sport who are having greatseasons, turning in performances that are much betterthan anyone might have anticipated, often are picturedon the cover of Sports Illustrated. Frequently, their performances then falter somewhat, leading some ath-letes to believe in a “Sports Illustrated jinx.” Similarly, it is common for phenomenal rookies to have less stel-lar second seasons—the so-called “sophomore slump.” While fans, athletes, and analysts have proposed many theories about what leads to such declines, a statisti-cian might offer a simpler (statistical) explanation. Explain.
Five soft drink bottling companies have agreed to implement a time management program in hopes of increasing productivity (measured in the cases of soft drinks bottled per hour). The number of cases of soft drinks bottled per hour before and after the implementation of the program are listed below: Before After 1 500 510 2 475 480 3 525 525, 4 490 495 5 530 533 a. State the appropriate null and alternative hypotheses to test whether the time management has been effective in increasing productivity. b. Calculate the value of the test statistics. c. Set up the appropriate rejection region for the hypotheses above, assuming a = 0.05. c. What is the appropriate conclusion? Justify your answer. d. Refer to Bottling Productivity Narrative. Find the approximate p-value.
In a simple random sample of 26 Kentucky alum, 23 believe that, despite their title dreams falling short in the Final Four in Indianapolis, the 2015 Wildcats are still the greatest team assembled in the 21st century.Test the hypothesis that more than 81% of Kentucky alum believe that the 2015 Wildcats are the greatest team assembled in the 21st century at the 0.05 level. The correct conclusion is that we 1. cannot 2.can 3.can maybe ..conclude that 1. exactly 2. more than 3.less than 4. a percentage different ...from 81% of 1. all 2. randomly selected 3. sampled ...Kentucky alum believe that the 2015 Wildcats are the greatest team assembled in the 21st century.What level of concern do you have for the validity of your results? Extreme −- we should not use any part of what we've done to make a conclusion None −- all assumptions are met so there appears to be no problem with the conclusion Moderate −- the sample size is only 26, but that's likely close enough to 30 for our results…
133) A large city installed LED streetlights, in part, to help reduce crime in particular areas. The city collected the number of property crimes along nine randomly selected streets in the month before and after the LED light installation, and claims that crime has been reduced. The crime data is shown in the table. Before LED After LED 17 14 25 20 10 14 14 12 16 8 34 35 32 27 21 18 14 12 a. Specify the competing hypotheses to test the city's claim. b. Calculate the value of the relevant test statistic and find the critical value at the 5% significance level. c. Does the evidence support the city's claim at the 5% significance level?
(e) Interpret the decision in the context of the original claim. Does it appear that peanut candies have weights that vary more than those of plain candies? O A. Since the null hypothesis is rejected, the weights appear to vary more for peanut candies. OC. Since the null hypothesis is not rejected, the weights appear to vary more for peanut candies. O B. Since the null hypothesis is not rejected, the weights do not appear to vary more for peanut candies. O D. Since the null hypothesis is rejected, the weights do not appear to vary more for peanut candies.
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