Sampling Distribution

Question

A variable of a population has a mean of μ=83 and a standard deviation of σ =21.
a) Identify the sampling distribution of the sample mean for samples of size 49.

b) In answering part(a), what assumption did you make about the distribution of the variable?

c) Can you answer part (a) if the sample size is 16 instead of 49? Why or why not?

Question

An operations manager who supervises an assembly line has been experiencing problems with the sequencing of jobs. The problem is that bottlenecks are occurring because of the inconsistency of sequential operations. He decides to conduct an experiment wherein two different methods are used to complete the same task. he measures the times (in seconds). The data are listed here. Can he infer that the second method is more consistent than the first method? Data are in file Xr13-61. 

Method 1: 8.8 9.6 8.4   9.0 8.3 9.2 9.0 8.7 8.5 9.4

Method 2: 9.2 9.4 8.9   9.6 9.7 8.4 8.8 8.9 9.0 9.7