Question Help * researcher studies water clarity at the same location in a lake

Question

Question Help * 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 the same dates 5 years later. The researcher immerses a weighted disk painted black and white and measures the depth (in inches) at hich it is no longer visible. The collected data is given in the table below Complete parts (a) and (b) below Observation 1 2 3 4 5 6 Date /25 3/19 530 7/3 9/13 11/7 686 672 579 57.6 60.2 70 After five years 698 69 8 686 65 2 680 757 (a) Why is it important to take the measurements on the same date? O A. Using the same dates maomaes the difference in water clarity. O B. Those are the same dates that all biologists use to take water clarity samples O C. Using the same dates makes the second sample dependent on the first O D. Using the same dates makes it easier to remember to take samples (b) Does the evidence suggest that the clanity of the lake is improving at the 0.05 level of significance? Note plot and boxplot of the data indicate that the differences are approximately normally distributed with no outiers. Choose the correct conclusion below O Reject Ho Dont reject Ho. Cick to select your anser enoVO Esc 2 3 4 5 6

Explanation / Answer

(a) It is important to take samples on the same data because using the same dates makes second sample dependent of first sample. Option C is correct.

(b) We will use paired data t test for dependent sample.

The difference table is given below.

Here,

H0 : d = 0

Ha : d > 0

dbar = 5.6833

Std. deviation of difference = 3.235

Standard error of difference se0 = 3/235/ sqrt(6) = 1.321

Test statistic

t = dbar /se0 = 5.6833/1.321 = 1.757

Here for dF = 6 -1 = 5 and alpha = 0.05

tcritical = t5,0.05 = 2.5706

so here t < tcritical so we shall reject the null hypothesis and can conclude that there is no difference in clarity in water level after 5 years.

Obs Initial after 5 years Difference (D) 1 68.6 69.8 1.2 2 67.2 69.8 2.6 3 57.9 66.6 8.7 4 57.6 65.2 7.6 5 60.2 69 8.8 6 70.5 75.7 5.2 Average 5.683 Std. Dev. 3.235

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