Question

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.

Answer 1

Answer:

The  number of rainfalls is $n =96$

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  $\sigma = 0.5$

     The  margin of error is  $E = 0.1$

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

                  $\alpha = 100 - 95$

                  $\alpha = 5 \%$

                 $\alpha =0.05$

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

Generally the sample size is mathematically represented as

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

substituting values

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

            $n =96$

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