Question

You need to compute the a 90% confidence interval for the population mean. How large a sample should you draw to ensure that the sample mean does not deviate from the population mean by more than 1.5? (Use 9.2 as an estimate of the population standard deviation from prior studies.)

Answer 1

Answer:

The sample size required is 102.

Step-by-step explanation:

The (1 - α)% confidence interval for population mean μ is:

$CI=\bar x\pm z_{\alpha/2}\times\frac{\sigma}{\sqrt{n}}$

The margin of error for this interval is:

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

Given:

σ = 9.2

(1 - α)% = 90%

MOE = 1.5

The critical value of z for 90% confidence level is:

$z_{0.10/2}=1.645$

*Use a z-table.

Compute the value of n as follows:

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

      $n=[\frac{z_{\alpha/2}\times \sigma}{MOE}]^{2}$

         $=[\frac{1.645\times 9.2}{1.5}]^{2}\\=101.795\\\approx102$

Thus, the sample size required is 102.