Question

Question 11 Answer saved Points out of 6.00 For the given margin of error and confidence level, determine the sample size required. A manufacturer of kitchen utensils wishes to estimate the proportion of left handed people in the population. Obtain a sample size that will ensure a margin of error of at most 0.041 for a 97% confidence interval. Show your answer as an integer value! P Pag question Answer:

Answer 1

The following information has been provided: (1)Margin of Error E = 0.041 (2)Level of significance α=0.03 (3)Since no estimate of the population proportion p is provided, we use the estimate p = 0.5 (which corresponds to the worst-case scenario). The critical value for the significance level α=0.03 is Zc =2.1701. This can be found by using either Excel or by using the normal probability table. The following formula is used to compute the minimum sample size required to estimate the population proportion p within the required margin of error: $n \ge p(1-p) \left( \frac{z_c}{E}\right)^2 =0.5*(1-0.5)\left(\frac{2.1701}{0.041}\right)^2 =700.3706$ Therefore, the sample size needed to satisfy the condition is n ≥ 700.3706, and it must be an integer number, we conclude that the minimum required sample size is ${\color{Purple} n = 701}$

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