A researcher takes measurements of water clarity at the same location in a lake

Question

A researcher takes measurements of 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 dates 5 years later. The researcher immerses a weighted disk painted black and white and measures the depth (in inches) at which it is no longer visible. The collected data is given in the accompanying table. Let X represent the initial depth and let Y represent the depth 5 years later. Does the evidence suggest that the clarity of the lake is improving at the 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 outliers. Date 1-25 3-19 5-30 7-3 9-13 11-7 Initial 35 63 68 75 57 34 51 After five vears 61 75 49 50 21. What is the test statistics? 17. What is the test function in calculators? a. Z- test b. T-test c. 1-PropZTest d. 2- PropZTest e. 2- SampTTest a. 1.3844 b. 1.3844 c. -0.8064 d. 0.8064 22. What is the p-value? a. 0.2283 b. -0.2283 c. -0.1124 d. 0.1124 18. What is testing? a. c. d. 23. What should we do? a. Reject the Ho b. Cannot reject the Ho c. Reject the H1 d. Accept the Ho 19. Two tailed, Right-tailed, or Left-tailed? a. Two-tailed b. Right-tailed c. Left-tailed 20. What is the critical value? 24. How to conclude? a.-2.5706 b. 2.5706 c. -2.0150 d. 2.0150 a. Evidence is found, so H1 is correct b. Evidence is found, so H1 is incorrect. c. Evidence is not found, so H1 is correct. d. Evidence is not found, so H1 is incorrect

Explanation / Answer

Output of the paired t test

below are null and alternate hypothesis
H0: mu1 - mu2 = 0
H1: mu1 - mu2 < 0 (Depth of lake is improved)

17)
2 - SampTTest

18)
Testing xbar

19)
Left tailed test

20)
ciritical value = -2.0150

21.
test statistics = -1.3844

22.
p-value = 0.1124

23.
Cannot reject H0

24.
Evidence is not found, so H1 is incorrect

t-Test: Paired Two Sample for Means Initial After 5 years Mean 55.33333333 60.83333333 Variance 295.4666667 176.9666667 Observations 6 6 Pearson Correlation 0.825952998 Hypothesized Mean Difference 0 df 5 t Stat -1.384405529 P(T<=t) one-tail 0.112417448 t Critical one-tail 2.015048373 P(T<=t) two-tail 0.224834897 t Critical two-tail 2.570581836

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