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The confidence interval approach reinforces the point that we can never prove an equality so we can never accept the null hypothesis. Failure to reject the null hypothesis could be due to two reasons: (a) Goldwater is biased but we have not obtained enough information. (b) Goldwater really is unbiased. Failure to obtain enough information can be rectified by taking an appropriate sample size, but before estimating the required size the chief analyst needs to know, from his practical and scientific knowledge, what size of bias he considers important.

2 THE NORMAL DISTRIBUTION 51 Uses of the normal distribution The normal distribution can be used for setting specifications. Having obtained a reliable estimate of the variability, the specification is set relative to a target mean using calculations illustrated in the above example. 1. 09 (approximately 3). 8% limits are widely used in process control. Another use of the normal distribution is in checking that a process or analytical method is in control. Using a normal probability plot, we can check whether a set of data is non-normal.

They have instructed Meg A. Byte to investigate the nature of the problem and suggest a course of action to reduce it. Meg first establishes that the problem is due to shortages of supplies but not due to procedural difficulties. Her next step is to analyse the data over time by computing box plots for the last 12 months. The box plots are shown below with the exception of April’s figures which consisted of a sample of 19 shipping times. These are shown below (in days). 22, 12, 17, 3, 15, 15, 14, 17, 11, 20, 16, 6, 24, 22, 42, 35, 19, 7, 28.

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