Answer:
The minimum sample size required is 207.
Step-by-step explanation:
The (1 - α) % confidence interval for population mean μ is:
[tex]CI=\bar x\pm z_{\alpha /2}\frac{\sigma}{\sqrt{n}}[/tex]
The margin of error of this confidence interval is:
[tex]MOE=z_{\alpha /2}\frac{\sigma}{\sqrt{n}}[/tex]
Given:
[tex]MOE=3\\\sigma=29\\z_{\alpha /2}=z_{0.01/2}=z_{0.05}=2.576[/tex]
*Use a z-table for the critical value.
Compute the value of n as follows:
[tex]MOE=z_{\alpha /2}\frac{\sigma}{\sqrt{n}}\\3=2.576\times \frac{29}{\sqrt{n}} \\n=[\frac{2.576\times29}{3} ]^{2}\\=206.69\\\approx207[/tex]
Thus, the minimum sample size required is 207.
