Chapter 8.3, Problem 83E

To determine

To find: The option that would have the smallest margin of error in computing the mean salt content $\mu$

Answer to Problem 83E

The correct option is (b).

Explanation of Solution

Given:

The confidence intervals are 90% and 95%

The sample sizes are 25, 50 and 100

The formula to compute the margin of error is:

  $\text{Margin of error}=z_{\alpha /2}\times \frac{\sigma }{\sqrt{n}}$

Here,

  $z_{\alpha /2}$ is the critical value which depends on the confidence level.

σ is the population standard deviation

n is the sample size

From the above written formula, it is clear that the confidence level and standard deviation are positively related. On the other hand, sample size is negatively related to the margin of error

For the smallest margin of error, smaller confidence level and large sample size are required. Here confidence level (90%) and sample size (50) are the perfect combination for the smallest margin of error.

Hence, the correct option is (b).