1. Consider a populationof adults in which 40% are aged 18-45, 32% are aged 45-65, and 28% are aged65+. Arthritis risk varies dramatically by age: 7% of 18-44 year olds have arthritis, while the proportionof adults with arthritis is 30% for the 45-64 age group, and 50% for the 65+ age group. If we drawan adult at random from this population and find out they have arthritis, what is the probabilitthey are 65+? Use Bayes'rule!

Percentage of population according to their age groups: P18-45 years=0.40P45-65 years=0.32P65+…

Answered: 1. Consider a population of adults in…

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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Example 17: In a sample of 1000 citizens of India, 540 are wheat eaters and the rest are rice eaters. Can we assume that both rice and wheat are equally popular in India at a%. level of significance?
1. Suppose the proportion of American adults who work at home is 40%. For a random sample of 100 American adults, what is the distribution of the sample proportion?
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new procedure is suggested for the manufacture of a piece of machinery. There areconcerns that the procedure might result in pieces that are shorter than the required length ofat least 10 cm. To research this, a random sample of 50 pieces was selected; the sample meanlength was 9.97 with a standard deviation of 0.1 cm. Does this suggest that the populationmean length of the pieces is less than the required 10 cm?a. Perform a hypothesis test at the 5% significance level. b. What type of error might have been made in the test above, type 1 or 2? Explain yourreasoning.
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Is the national crime rate really going down? Some sociologists say yes! They say that the reason for the decline in crime rates in the 1980s and 1990s is demographics. It seems that the population is aging, and older people commit fewer crimes. According to the FBI and the Justice Department, 70% of all arrests are of males aged 15 to 34 yearst. Suppose you are a sociologist in Rock Springs, Wyoming, and a random sample of police files showed that of 34 arrests last month, 25 were of males aged 15 to 34 years. Use a 10% level of significance to test the daim that the population proportion of such arrests in Rock Springs is different from 70%. A USE SALT (a) What is the level of significance? State the null and alternate hypotheses. O H P 0.7 O H.: p - 0.7; H,: p 5 and ng > S. O The standard normal, since np > 5 and ng > 5. O The Student's t, since np
In one particular rainforest in Tasmania, it has been found that 70% of the trees are eucalyptus trees; 20% of the trees are Australian blackwood trees and 10% of the trees are myrtle beech trees. Unfortunately, this rainforest has recently been affected by bushfires; and we are interested in determining whether or not the above percentage distribution of trees has been affected by these bushfires. When the number of trees remaining were counted after several had been burnt down by the bushfires, it was found that there were a total of 500 trees left. Of these, 320 were eucalyptus trees; 120 were Australian blackwood trees and 60 were myrtle beech trees. A scientist would like to know if there is evidence of a significant change in the percentage distribution of trees aş a result of these unfortunate bushfires. (i) Use statistical notation to state the appropriate null and alternate hypotheses. (ii) Calculate the chi-squared test statistic for these data. (ii1) Given a p-value of 0.038…
2. A study for adverse reactions assigned adults at random to one of two common pain relievers (ibuprofen and acetaminophen). It was found that out of 733 adults who were administered ibuprofen, 103 of them experienced an adverse reaction, and out of 732 adults who were administered acetaminophen, 85 of them experienced an adverse reaction. Let p1 denote the proportion of adults who experience an adverse reaction when taking ibuprofen and let p2 denote the proportion of adults who experience an adverse reaction when taking acetaminophen. Suppose we want to answer the following questions. i) Test, at the 3% level of significance, whether the proportion of adults who experience an adverse reaction when taking ibuprofen is greater than the proportion of adults who experience an adverse reaction when taking acetaminophen. ii) Calculate the 97% confidence interval for p1 - P2. The table below provides the information needed to perform the hypothesis test: Value x1 103.0000 85.0000 733.0000…

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