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From a random sample of 58 businesses, it is found that the mean time the owner spends on administrative issues each week is 20.53 with a population standard deviation of 3.23. What is the 95% confidence interval for the amount of time spent on administrative issues?

User McBob
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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:


  • Mean (X) = 20.53

  • Population standard deviation (σ) = 3.23

  • Sample size (n) = 58

  • 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.

User Paul Bica
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