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 themeasements on the same dates 5 years later. The earcher 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 letY represent the depth 5 years later. Complete parts (a) through (c) below. 囲Click the icon to view the water clarity data.

1. What is the t-statistic?

2. What is the p -value?

3. What is the conclusion.

Answer 1

1)

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

t-Test: Paired Two Sample for Means
	initial	5 years
Mean	52.83333333	59
Variance	233.3666667	106
Observations	6	6
Pearson Correlation	0.802392777
Hypothesized Mean Difference	0
df	5
t Stat	-1.619756333
P(T<=t) one-tail	0.083105014
t Critical one-tail	2.015048373
P(T<=t) two-tail	0.166210029
t Critical two-tail	2.570581836

this is 1-tailed test

1. What is the t-statistic?

-1.6197

2. What is the p -value?

0.08310501

3. What is the conclusion.

since p-value > 0.05

we fail to reject the null that is Cannot reject H0

Evidence is not found, so H1 is incorrect

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