Final answer:
To calculate the 95% confidence interval for the mean time spent on administrative issues, use the sample mean of 20.53, the population standard deviation of 3.23, the sample size of 58, and the z-score of 1.96. The margin of error is then computed and used to find the upper and lower limits of the interval.
Step-by-step explanation:
To find the 95% confidence interval for the mean amount of time business owners spend on administrative issues, we will use the z-distribution because the population standard deviation is known. For a 95% confidence interval, the z-score that corresponds is approximately 1.96 (this can be found on a standard z-table or using statistical software).
The formula for a confidence interval is given by: mean ± (z-score * (population standard deviation/sqrt(sample size))). Thus, we plug in the values provided:
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- Mean (X) = 20.53
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- Population standard deviation (σ) = 3.23
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- Sample size (n) = 58
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- Z-score for 95% confidence = 1.96
We calculate the margin of error (ME): ME = 1.96 * (3.23/sqrt(58)), and then add and subtract this margin of error from the sample mean to determine the confidence interval.
The confidence interval estimate is: 20.53 ± ME.