Final answer:
Reducing the acceptance number c in a sampling plan while keeping the sample size n constant makes the sampling plan stricter without changing the standard deviation of the sampling distribution. The reduced c value increases the chance of rejecting a batch, which could lead to a higher Type I error rate. Increasing the sample size would be a method to reduce sampling distribution variability and enhance precision.
Step-by-step explanation:
When maintaining a constant sample size denoted as n, and reducing the acceptance number c, the implication is that you are allowing fewer defects or errors before a batch is rejected in the context of quality control sampling. This has the effect of making the sampling plan stricter, as fewer defects are tolerated, which can lead to a higher likelihood of rejecting the batch even if the actual quality of the product doesn't change.
From a statistical perspective, the standard deviation of the sampling distribution of the means, often represented as the variability among sample means, will not change as c is changed, because it is solely a function of the sample size n and the population standard deviation.
To ensure a tighter control and reduce the probability of accepting a bad batch (Type II error), one might want to consider increasing the sample size n, which would help decrease the standard deviation of the sampling distribution, thereby making the mean estimate more precise as suggested by the equation Za / √n, where Za represents the z-score corresponding to the desired confidence level.