1. What is the t-statistic? 2. What is the p -value? 3. What is the conclusion.

Question

1. What is the t-statistic?

2. What is the p -value?

3. What is the conclusion.

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. Click the icon to view the water clarity data.

Explanation / Answer

1)

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

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

Please rate

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

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