A random sample of 10 shipments of stick-on labels showed the following order sizes. 12,000 18,000 30,000 60,000 14,000 10,500 52,000 14,000 15,700 19,000 Click here for the Excel Data File (a) Construct a 95% confidence interval for the true mean order size. (Round your standard deviation answer to 1 decimal place and t-value to 3 decimal places. Round your answers to the nearest whole number.) The 95% confidence interval to

(a) 95% confidence interval for the true mean order size =  [ 11972.22 , 37067.80 ]

Step-by-step explanation:

We are given a random sample of 10 shipments of stick-on labels with following order sizes;

12,000, 18,000, 30,000, 60,000, 14,000, 10,500, 52,000, 14,000, 15,700, 19,000

Firstly, Sample mean, =

  = = 24520

Sample standard deviation, s = = 17541.81

The pivotal quantity for confidence interval is given by;

            P.Q. = ~

So, the 95% confidence interval for true mean order size is given by;

P(-2.262 < < 2.262) = 0.95

P(-2.262 < < 2.262) = 0.95

P(-2.262 * < < 2.262 * ) = 0.95

P(Xbar - 2.262 * < < Xbar + 2.262 * ) = 0.95

95% confidence interval for = [ Xbar - 2.262 * , Xbar + 2.262 * ]

                                           = [ 24520 - 2.262* ,  24520 - 2.262* ]

                                           = [ 11972.22 , 37067.80 ]

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