Question

The U.S. Census Bureau would like to estimate the average square footage of a new single-family home with a 95% confidence interval and a margin of error within plus or minus 100 square feet. Assuming the standard deviation for the square footage of new single-family homes is 850 square feet, the required sample size is ________.

Answer 1

Answer:

The sample size is  $n =278$

Step-by-step explanation:

From the question we are told that

    The margin of error is  $E = 100$

    The standard deviation is  $\sigma = 850$

Given that the confidence level is  95% then the level of significance is mathematically represented as

       $\alpha = (100-95)\%$

       $\alpha =0.05$

Next we obtain the critical value  $\frac{\alpha }{2}$ from the normal distribution table  

  The value  is  $Z_{\frac{\alpha }{2} } = 1.96$

Generally the sample size is mathematically represented as

       $n = \frac{(Z_{\frac{\alpha }{2}})^2}{E^2} * \sigma^2$

=>   $n = \frac{(1.96)^2}{100^2} * 850^2$

=>    $n =278$