Answer:
The minimum sample size required is 1041.
Step-by-step explanation:
Assume that the proportion of West Coast consumers who would spend at least $30 on Willamette Valley be 50%.
That is, p = 0.50.
The margin of error is computed using the formula:
[tex]MOE=z_{\alpha /2}\sqrt{\frac{p(1-p)}{n} }[/tex]
Given:
MOE = 0.04
Critical value = [tex]z_{\alpha /2}=z_{0.01/2}=z_{0.005}=2.58[/tex]
*Use the z-table for the critical value.
Compute the value of n as follows:
[tex]MOE=z_{\alpha /2}\sqrt{\frac{p(1-p)}{n} }\\0.04=2.58\times\sqrt{\frac{0.50(1-0.50)}{n} }\\0.0155=\sqrt{\frac{0.25}{n} }\\n=\frac{0.25}{(0.0155)^{2}} \\=1040.58\\\approx1041[/tex]
Thus, the minimum sample size required is 1041.
