Question

4. Five samples of a ferrous-type substance are to be used to determine if there is a difference between a laboratory chemical analysis and an X-ray fluorescence analysis of the iron content. Each sample was split into two subsamples and the two types of analysis were applied. Following are the coded data showing the iron contents analysis: Sample Analysis X-ray Chemical 2.3 2.1 2.0 1.9 2.4 2.4 2.5 23 Using a paired test, determine at the 0.05 level of significance whether the two methods of analysis give, on the average, the same result. Assume that the populations are normal. Do not execute; instead, answer the questions below. Appropriate symbols must be used below where applicable. a) 1) Define (describe) the random variable and 2) characterize the population. b) Summarize the sample data, using the appropriate notation. c) State 1) the parameter of interest and 2) its point estimator symbolically. 1) d) State the 1) null and 2) alternate hypotheses. e) Uniquely identify the appropriate test statistic that would be used for a hypothesis test. If additional assumptions are necessary, list them. Briefly justify your selection.

Answer 1

a I Huse the underlying variable is d = x-4 where x denotes on content in Sample 1 using X-ray analysis, y is in content in samlyle 1 using chemical analysis. d denotes de note difference in measurements of iron content wing two methods 2) The population of cliffenes in measurement of iron contents follows normal

distorbution hypornais similao and some with 20 mean (undu hall that inan content is almost cosing to analysis methods ) unknown varianca oz. b) mean of differences in measurements and standard deviation of difference Cluse of internet in calculating tegt Stapstic ♡ 22 1.9 175 173 2.4 d Ho-2 1-0.1-0.2 -0.2.0. det 6.0036/0.0/0.00360.00360.0196 T es sample mean of differences & (n is part of observations) Ed -0.7 s- =-0.14 So is s'ample standand deviation = {(d-H) VOL = 0.032 - 0.0894

7 The test statistic t- ě = salvo is 0.14 0.asqulus The asgeimplins are that The population of differences in measurement follows normal doribution, ů . The sample case dependent . x say inon contrast B Conselated with Chemical iron content.