Question

9.The mean of a certain production process is known to be 50 with a standard deviation of 2.5. The production manager may welcome any change is mean value towards higher side but would like to safeguard against decreasing values of mean. He takes a sample of 12 items that gives a mean value of 48.5. What inference should the manager take for the production process on the basis of sample results? Use 5 per cent level of significance for the purpose.

Answer 1

Solution:-

Mean = 50 , Std dev = 2.5

5% level of Sig <=> 95% level of confidence

We have values segregated towards two standard deviation for a 95% level of confidence . So finding the range we get

Mean +- 2 * std dev is the Mean range where values should rise for the production manager.

50 - 2* 2.5 < Mean < 50 + 2*2.5 <

50 - 5 < Mean < 50+5

45 < Mean < 55

So , the production manager mean of the sample is a significant one and follows the normal distribution of the given population data but the major point of concern in here is that the sample size chosen is too small and a minor change in the same would lead to a significant change.