Mathematics: How large a sample must we take if we want the margin of error to be at most 0.01 pound with 95% confidence

How large a sample must we take if we want the margin

carriboneman

06.02.2022

The sample size is n = 153664

Step-by-step explanation:

From the question we are told that

The margin of error is E = 0.01

From the question we are told the confidence level is 95% , hence the level of significance is

$\alpha = (100 - 95 ) \%$

=> $\alpha = 0.05$

Generally from the normal distribution table the critical value of $\frac{\alpha }{2}$ is

$Z_{\frac{\alpha }{2} } = 1.96$

Let take the standard deviation to be $\sigma = 2 \ pounds$

Gnerally the sample size is mathematically represented as

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

=> $n = [\frac{1.96 *2 }{0.01} ]^2$

=> n = 153664

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