Stats c The isotopic abundance ratio of natural silver (Ag) is the ratio of thestable isotopes Ag107 to Ag109. Its mean is 1.076, and measurements ona random sample of observed isotopic abundance ratios suggested thatthey are plausibly normally distributed with a sample standarddeviation of 0.0026. Interest in this part of the question concerns theplanning of a further experiment to detect whether this ratio is differentin observations from a certain source of silver nitrate.The new study will use a two-sided test at the 5% significance level,assuming normality. It is desired to make sufficient observations of theisotopic abundance ratio on the silver nitrate so that the power of thetest to distinguish a difference between the null hypothesis of a trueunderlying mean of 1.076 and a value that is 0.0015 larger or 0.0015smaller is 90%. For the purpose of performing the necessary sample sizecalculation, it will be assumed that the population standard deviation ofthe isotopic abundance ratio measurements is equal to the samplestandard deviation given above.(i) Calculate, by hand, the size of the sample required to achieve thedesired power of the test. Show your working.(ii) Suppose that it was decided to seek to distinguish between theunderlying mean and values that are two-thirds as much (that is,0.001) larger or smaller than it (rather than 0.0015). Ignoringrounding up to an integer, and assuming that no other aspect ofthe problem changes, by what factor should the required samplesize be adjusted?

Answered: sotopes Ag107 to Ag. Its mean is 1.076,…

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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Fluoride Exposure in Drinking Water Exercise 2.250 introduces a study showing that fluoride exposure might have long-term negative consequences for the offspring of pregnant women. Part of the study examines the effect of adding fluoride to tap water on mean fluoride concentration in women. Summary statistics for fluoride concentration (measured in mg/L) for the two groups are given in the table below. Tap water Fluoridated Non-fluoridated Conclusion: Sample size 141 228 Mean 0.69 0.40 St.Dev. 0.42 0.27 Find and interpret a 99% confidence interval for the mean increase in fluoride concentration for those with fluoridated tap water. Let Group 1 represent those with fluoridated tap water and Group 2 represent those without fluoridated tap water. Confidence interval: i to i (round to three decimal places)
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1.3.2 Consider the output given below that was obtained using the One Proportion applet. Use information from the output to find the standardized statistic for a sample propor- tion value of 0.45. Probability of success (n): 0.30 Sample size (n): 25 Number of samples: 1000 O Animate Draw Samples Total = 1000 180 Mean = 0.301 SD = 0.091 120 60 0.08 0.16 0.24 0.32 0.40 0.48 0.56 0.64 Proportion of success
10.34 The resistances of a certain type of thermistor are specified to be normally distributed with a mean of 10,000 ohms and a standard deviation of 500 ohms, at a temperature of 25°C. Thus, only about 2.3% of these thermistors should produce resistances in excess of 11,000 ohms. The exact measurement of resistances produced is time-consuming, but it is easy to determine whether the resistance is larger than a specified value (say, 11,000). For 100 ther- mistors tested, 5 showed resistances in excess of 11,000 ohms. Do you think the thermistors from which this sample was selected fail to meet the specifications? Why or why not?
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