Suppose that you want to estimate the mean pH of rainfalls in an area that suffers from heavy pollution due to the discharge of smoke from a power plant. Assume that σ is in the neighborhood of .5 pH and that you want your estimate to lie within .1 of µ with probability near .95. Approximately how many rainfalls must be included in your sample (one pH reading per rainfall)? Would it be valid to select all of your water specimens from a single rainfall? Explain.

The answer to the second question is no it will not be valid this because from the question we are told that the experiment require one pH reading per rainfall so getting multiply specimens(used for the pH reading) from one rainfall will make the experiment invalid.

Step-by-step explanation:

from the question we are told that

The standard deviation is [tex]\sigma = 0.5[/tex]

The margin of error is [tex]E = 0.1[/tex]

Given that the confidence level is 95% then we can evaluate the level of significance as

[tex]\alpha = 100 - 95[/tex]

[tex]\alpha = 5 \%[/tex]

[tex]\alpha =0.05[/tex]

Next we will obtain the critical value of [tex]\frac{\alpha }{2}[/tex] from the normal distribution table , the value is [tex]Z_{\frac{\alpha }{2} } = 1.96[/tex]

Generally the sample size is mathematically represented as

[tex]n = [\frac{Z_{\frac{\alpha }{2} * \sigma }}{ E} ]^2[/tex]

substituting values

[tex]n = [\frac{1.96 * 0.5 }{ 0.1} ]^2[/tex]

[tex]n =96[/tex]

The answer to the second question is no the validity is null this because from the question we are told that the experiment require one pH reading per rainfall so getting multiply specimens(used for the pH reading) from one rainfall will make the experiment invalid