Probability math

Question

A chemist makes repeated measurements of the pH value in two lakes, A and B. The measurements are affected by random error that is normally distributed. The results are given by the following table.

A: 6.6 6.4 6.7 6.9

B: 7.2 6.8 7.0 7.2

Setermine this by calculating an appropriate confidence interval. Use confidence level 95%.

Do the two lakes have different pH values?

Answer 1

The pH of the first lake is, at the

95% Confidence Level, 1.960s_x̄

Margin of Error: 6.65 ±0.204 (±3.07%).

And the pH of the second lake is, at the

95% Confidence Level, 1.960s_x̄

Margin of Error: 7.05 ±0.188 (±2.66%)

The upper limit for the first lake is 6.65 + 0.204 = 6.854

The lower limit for the second lake is 7.05 - 0.188 = 6.862

Since the values do not overlap, they cannot be considered to be equal at the 95% confidence level.

s_x̄ = s / √N