Question

We want to estimate acidity of rainfall. Assume that σ is in the neighborhood of 0.5 pH and that you want your estimate to lie within 0.1 of µ with probability near 0.95. How many rainfalls must be included in your sample (one pH reading per rainfall)?

Answer 1

Answer:

The number of rainfalls required to be included in the sample is 97.

Step-by-step explanation:

The information provided is:

Error = E = 0.1

Standard deviation = σ = 0.5

1 - α = 0.95

α = 0.05

The error formula is:

$E=z_{\alpha /2}\times\frac{\sigma}{\sqrt{n}}$

Compute the critical value as follows:

$z_{\alpha/2}=z_{0.05/2}=z_{0.025}=1.96$

*Use the z-table for the critical value.

Compute the value of n as follows:

$E=z_{\alpha /2}\times\frac{\sigma}{\sqrt{n}}\\0.1=1.96\times\frac{0.5}{\sqrt{n}} \\n=(\frac{1.96\times0.5}{0.1} )^{2}\\=96.04\\\approx97$

Thus, the number of rainfalls required to be included in the sample is 97.