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Based on these sample statistics, compute the 95% confidence interval for the average delivery time. a.[15.366, 25.754]b.[20.159, 25.754]c.[20.195, 20.169]d.[ 20.159, 20.961]

Question

Based on these sample statistics, compute the 95% confidence interval for the average delivery time. a.[15.366, 25.754]b.[20.159, 25.754]c.[20.195, 20.169]d.[ 20.159, 20.961]

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Solution

To compute the 95% confidence interval for the average delivery time, we can use the formula for the confidence interval:

CI = x̄ ± Z * (s/√n)

where:

  • x̄ is the sample mean (20.56 minutes),
  • Z is the Z-score for the desired confidence level (for a 95% confidence level, Z is approximately 1.96),
  • s is the sample standard deviation (2.65 minutes), and
  • n is the sample size (168 orders).

First, calculate the standard error (SE), which is the standard deviation divided by the square root of the sample size:

SE = s/√n = 2.65/√168 ≈ 0.2037

Then, calculate the margin of error (ME), which is the Z-score multiplied by the standard error:

ME = Z * SE = 1.96 * 0.2037 ≈ 0.3993

Finally, calculate the confidence interval:

CI = x̄ ± ME = 20.56 ± 0.3993

So, the 95% confidence interval for the average delivery time is approximately [20.1607, 20.9593] minutes.

Therefore, the answer is d. [20.159, 20.961].

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