Question

Need help answering this question. All work must be shown(where needed) to receive credit.

3. How large a sample must be drawn so that a 98% confidence interval for u will have a margin of error equal to $133 and o = $530.

Answer 1

Provided that the margin of error is 133, the population standard deviation σ is 530, and the significance level is specified at 0.02, we can compute the minimum required sample size by using the following formula:

$n \ge \left( \frac{z_c \sigma}{E}\right)^2$

At 2% level of significance, we have Zc = 2.326

$\rightarrow n \ge \left( \frac{2.326 *530}{133}\right)^2$

$\rightarrow n \ge \left( 9.269)^2$

$\rightarrow n \ge 85.91477915$

Hence n should be:

${\color{DarkRed} n = 86}$

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