The average time in data to process orders received by a metal fabrication company is to be estimated. A sample of
20 orders is randomly selected from a total of 200 orders processed over a
6 month period and the sample mean is
5.4 days with a standard deviation of 1.2 days. compute a 90 percent confidence interval of the estimated average processing time.
I know from my sheet that 90%= 1.64
please help
You have everything you need to calculate the confidence interval.
Formula:
CI90 = mean + or - 1.64 (sd/√n)
Using your data:
CI90 = 5.4 + or - 1.64 (1.2/√20)
Finish the calculation to determine the interval.
To determine the interval, you need to calculate the values.
First, let's calculate the standard error (SE):
SE = standard deviation / square root of the sample size
SE = 1.2 / √20 ≈ 0.2689
Next, calculate the margin of error (ME) using the critical value, which is 1.64 for a 90% confidence level:
ME = critical value * SE
ME = 1.64 * 0.2689 ≈ 0.4409
Finally, calculate the confidence interval:
CI90 = sample mean ± ME
CI90 = 5.4 ± 0.4409
Now, you can express the confidence interval as:
CI90 ≈ (4.96, 5.84)
Therefore, with 90% confidence, the estimated average processing time for orders received by the metal fabrication company is between 4.96 and 5.84 days.