Question

A researcher studies water clarity at the same location in a lake on the same dates during the course of a year and repeats the measurements on the same gates 5 years later. The researcher immerses a weighted disk painted black and white and measures the depth on inches) at which it is no longer visible. The collected data is given the table below. Complete parts (a) through (c) below Observation 1 2. 3 4 5 6 Date 1/253/195/30 7/3 9/13 11/7 Initial Depth, X 402 50.1 46.3 744 50.4 64.1 Death Five Years Later, 46.4 483 498 71.7 54.9 80.6 Click the icon to view the table of critical values a) Why is it important to take the measurements on the same date? OA. Using the same dates makes it easier to remember to take samples OB. Using the same dates maximizes the difference in water clarity OC. Using the same dates makes the second sample dependent on the first and reduces variability in water clarity attributable to date. OD. Those are the same cates that all biologists use to take water clarity samples b) Does the evidence suggest that the clarity of the lake is improving on the a= 0.05 level of significance? Note that the normal probability plot and boxplot of the data indicate that the differences are approximately normally distributed with no outiers Lex - YIdentity the nul and warrative hypotheses Home Hiro Down

Answer 1

a) Ans: C b) Water clarity improved if and only if depth measured is increased. so, since di = Xi – Yi, if clarity improves then di < 0 so, Ho: pid=0 H1: Hd < 0 d-0 test stat ttest n = 6, d = -1.033, S4 = 4.1788 so, ttest = -0.61, tcritical,df=5 -2.02 Conclusion : Fail to reject Ho. There is IN SUFFICIENT evidence at the a= 0.05, .... c) R – code for borplot : Ans: D Sa/Vn

> x<-c(40.2,50.1,46.3,74.4,50.4,64.1)
> y<-c(46.4,48.3,49.8,71.7,54.9,60.6)

> d<-x-y
> d
[1] -6.2 1.8 -3.5 2.7 -4.5 3.5

> boxplot(d,horizontal = T)

-6 -4 -2 0 2