***EXPLICITLY PUT THE LOWER AND UPPER BOUND A simple random sample of size n = 4

Question

***EXPLICITLY PUT THE LOWER AND UPPER BOUND

A simple random sample of size n = 400 individuals who are currently employed is asked if they work at home at least once per week. Of the 400 employed individuals surveyed, 31 responded that they did work at home at least once per week. Construct a 99% confidence interval for the population proportion of employed individuals who work at home at least once per week. The lower bound is .(Round to three decimal places as needed.) The upper bound is .(Round to three decimal places as needed.)

Explanation / Answer

n = 400    

p = 31/400 = 0.0775    

% = 99    

Standard Error, SE = {p(1 - p)/n} =    (0.0775(1 - 0.0775))/400 = 0.013369158

z- score = 2.575829304    

Width of the confidence interval = z * SE =     2.57582930354892 * 0.0133691576024819 = 0.03443667

Lower Limit of the confidence interval = P - width =     0.0775 - 0.0344366679162367 = 0.043

Upper Limit of the confidence interval = P + width =     0.0775 + 0.0344366679162367 = 0.112

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