Answer:
<em>a)Sample size would be required to obtain a margin of error of 1 days is </em>
<em>n = 179</em>
<em>b) sample size would be required to obtain a margin of error of 2.5 days is n = 20</em>
<u>Step-by-step explanation</u>:
<u><em>step(i):</em></u>-
Given Population standard deviation = 6.83 days
a) Given margin of error = 1 day
<em>The margin of error is determined by</em>
<u><em>Step(ii):</em></u>-
<em>Given 95 % of confidence level</em>
<em>Now the critical value Z₀.₀₅ = 1.96</em>
<em></em><em></em>
<em>√n = 13.38</em>
<em>Squaring on both sides, we get</em>
<em>n = 179.206</em>
<em>b)</em>
<em>step(i):-</em>
a) Given margin of error = 2.5 day
<em>The margin of error is determined by</em>
<u><em>Step(ii):</em></u>-
<em>Given 90 % of confidence level</em>
<em>Now the critical value Z₀.₁₀ = 1.645</em>
<em></em><em></em>
Cross multiplication , we get
√n = 4.494
<em>Squaring on both sides, we get</em>
<em>n = 20.19</em>
<em></em>
<u><em>Final answer</em></u><em>:-</em>
<em>a)Sample size would be required to obtain a margin of error of 1 days is </em>
<em>n = 179</em>
<em>b) sample size would be required to obtain a margin of error of 2.5 days is n = 20</em>