Question

It costs more to produce defective items - since they must be scrapped or reworked - than it does to produce non-defective items. This simple fact suggests that manufacturers should ensure the quality of their products by perfecting their production processes instead of depending on inspection of finished products. In order to better understand a particular metal stamping process, a manufacturer wishes to estimate the mean length of items produced by the process during the past 24 hours. a) How many parts should be sampled in order to estimate the population mean to within 0.1 millimeter (mm) with 95% confidence? Previous studies of this machine have indicated that the standard deviation of lengths produced by the stamping operation is about 2.2 mm Enter a number b) Time permits the use of a sample size no larger than 100, if a 90% confidence interval for the mean is constructed with n = 100, will it be wider or narrower than would have been obtained using the sample size determined in part a? O wider unchanged cannot be determined narrower

Answer 1

Let the margin of error be E = 0.1. Let the standard deviation be o = 2.2. Let the level of significance be a =0.05. Let the critical z-value obtained from standard normal table be = 7 = 2005 = 1.96. 7 The sample size is obtained as follows: Gxd n= 2 1.962x2.22 0.12 =1859.33 - 1860

The margin of error for a 90% confidence interval for the mean constructed with sample size 100 and standard deviation 2.2 is given as follows: =1.645200 = 0.3619 The margin of error is higher when the sample size decreases. Therefore, it can be concluded that the 90% confidence interval will be wider when the sample size decreases to n= 100.