In solving for the root of a single equation, the approximate value obtained after the third iteration is 0.34376 and the value obtained after the fourth iteration is 0.34225. If the stopping criterion is E, S 1%, which of the following of the following is the valid next step? a. Stop iteration and conclude that x. b. Continue iteration and let x, be the next input value. c. Stop iteration and continue with another root finding technique. d. Continue iterations up to x, only. OB OD
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- For the situation described below, state the null and alternative hypotheses to be tested. (Enter != for ≠ as needed.) A seed wash is expected to change the proportion p of seeds that germinate when planted in poorly-draining soil. Suppose that the current germination rate is about 70%.To see the effect of a relatively small error in the estimate of the amount of carbon-14 in a sample being dated, consider this hypothetical situation: a. A bone fragment found in central Illinois in the year 2000 contains 17% of its original carbon-14 content. Estimate the year the animal died. b. Repeat part (a), assuming 18% instead of 17%. c. Repeat part (a), assuming 16% instead of 17.People having Raynauds syndrome are apt to suffer a sudden impairment of blood circulation in fingers and toes. In an experiment to study the extent of this impairment, each subject immersed a forefinger in water and the resulting heat output (cal/cm2/min) was measured. For m = 12 subjects with the syndrome, the average heat output was x = 0.64, and for n = 12 non-sufferers, the average output was 2.05. Let µ1 and µ2 denote the true average heat outputs for the two types of subjects. Assume that the two distributions of heat output are normal with σ1 = 0.2 and σ2 = 0.2. 1) Consider testing H0: µ1 − µ2 = 0 versus Ha: µ1 − µ2 < 0 at level 0.01. Describe in words what Ha says, and then carry out the test. 2) What is the probability of a type II error when the actual difference between µ1 and µ2 is µ1 − µ2 = −1.2? 3) Assuming that m=n, what sample sizes are required to ensure that β=0.1when µ1− µ2 = −1.2?
- A local gas station has developed a new lottery scratch card in which they want 20% of contestants to win a small prize, 5% of contestants to win a medium prize, and 1% of contestants to win a large prize. If the scratch card costs buyers $5, determine how much each prize should award if the store wishes to make a long-run average of $1 for each scratch card sold (solve using R if possible)Researchers interested in lead exposure due to car exhaust sampled the blood of 52 police officers subjected to constant inhalation of automobile exhaust fumes while working traffic enforcement in a primarily urban environment. The blood samples of these officers had an average lead concentration of 124.32 µg/l and a SD of 37.74 µg/l; a previous study of individuals from a nearby suburb, with no history of exposure, found an average blood level concentration of 35 µg/l. Based on your preceding result, without performing a calculation, would a 99% confidence interval for the average blood concentration level of police officers contain 35 µg/l? Based on your preceding result, without performing a calculation, would a 99% confidence interval for this difference contain 0? Explain why or why not.For a population with µ = 40 and σ = 8, what is the X value corresponding to z = 1.50?
- The owner of Kat Motel wants to develop a time standard for the task of cleaning a cat cage. In a preliminary study, she observed one of her workers perform this task six times, with the following results: Observation 1 2 3 4 5 6 Time(Seconds) 99 87 90 81 93 90 _____ is the standard time for this task if the employee worked at a 150 PRF, and an allowance of 20 percent of job time is used. _____ is the normal time for this task if the employee worked at 150 PRF. _____ is the standard time for this task if the employee worked at a 150 PRF and an allowance of 10 percent of the workday is used.A new insecticide is advertised to kill more than 95% roaches upon contact. In a laboratory test, the insecticide was applied to 400 roaches and 384 died immediately after contact. Is this sufficient evidence to support the advertised claim? Use α=0.05. (c) p-value for the problem above iA manufacturer of floor polish conducted a consumer-preference experiment to determine which of five different floor polishes was the most appealing in appearance. A sample of 100 consumers viewed five patches of flooring that had each received one of the five polishes. Each consumer indicated the patch he or she preferred. The lighting and background were approximately the same for all patches. The results are given below. Solve the following using the p-value approach and solve using the classical approach. Polish A B C D E Total Frequency 26 16 16 21 21 100 (a) Complete the hypothesis test using ? = 0.10. (i) Find the test statistic. (Round your answer to two decimal places.) (ii) Find the p-value. (Round your answer to four decimal places.)
- A manufacturer of floor polish conducted a consumer-preference experiment to determine which of five different floor polishes was the most appealing in appearance. A sample of 100 consumers viewed five patches of flooring that had each received one of the five polishes. Each consumer indicated the patch he or she preferred. The lighting and background were approximately the same for all patches. The results are given below. Solve the following using the p-value approach and solve using the classical approach. Polish A B C D E Total Frequency 26 16 14 20 24 100 (a) State the hypothesis for "no preference" in statistical terminology. H0: P(A) + P(B) + P(C) + P(D) + P(E) = 1H0: P(x) = P(y) for some x and y H0: P(A) ≠ P(B) ≠ P(C) ≠ P(D) ≠ P(E)H0: P(A) = P(B) = P(C) = P(D) = P(E) = 0.2 (b) What test statistic will be used in testing this null hypothesis? p? ?2tz (c) Complete the hypothesis test using ? = 0.10.(i) Find the test statistic. (Round your answer to two decimal…A manufacturer of floor polish conducted a consumer-preference experiment to determine which of five different floor polishes was the most appealing in appearance. A sample of 100 consumers viewed five patches of flooring that had each received one of the five polishes. Each consumer indicated the patch he or she preferred. The lighting and background were approximately the same for all patches. The results are given below. Solve the following using the p-value approach and solve using the classical approach. Polish A B C D E Total Frequency 24 19 13 21 23 100 (c) Complete the hypothesis test using a = 0.10.(i) Find the test statistic. (Round your answer to two decimal places.)(ii) Find the p-value. (Round your answer to four decimal places.)In a certain suburb of Montréal, residents have expressed their worries about the quality of the air. Of particular concern is the concentration (in μg/m3) of particulate matter smaller than 2.5 μm in size (PM2.5). The environmental standard is a PM2.5 concentration of 15 μg/m3 or less. 9-a) To conduct this study, Thomas installs 25 PM2.5 detectors at different locations in the suburban area. Each detector will provide one reading of PM2.5 concentration at a given time. With 25 detectors, what is the probability that Thomas declares the sample mean of PM2.5 concentrations significantly greater than the environmental standard while the population mean is 16 μg/m3? The population variance is assumed to be known and equal to 9. Use α = 0.01. 9-b) Thomas is interested to purchase a new and cheaper instrument to measure PM2.5 concentration. He is worried, however, that the precision of the new instrument may be lower than that of the current one. To be acceptable, the standard…