1. Given the following process control data for a quality attribute (three samples of size 400 each):

Sample	Defectives
#1	36
#2	32
#3	52

a) If the process or population proportion of defectives is unknown, what is its estimated value ? (Note: The population or process proportion is NOT given, but we estimate it by using the expected value of the sample proportion-simply average the given sample proportions and this is your process or population proportion

b) Hypothetically speaking, if this process is known to produce 11 percent defectives on average, using 3 control limits, do any of the sample proportions indicate that the process is out of control, viz., that there is the existence of assignable-cause variation ? (Use the binomial distributions mean and S.D. for calculating the upper and lower control limits)

1. What is the operational implication of the Type 1 error or so-called Alpha Risk ? Depict what we mean by Type 1 error on a diagram of the standard normal distribution. Please ensure that you precisely label the Critical Region (set of values of the sample statistic pertinent to rejection of H₀, the null hypothesis). Explain the primary difference between Type 1 and Type 2 errors and which of them is likely to cause a greater problem for an Operations Manager /Industrial Engineer ?

1. Given the following process control data for a normally distributed quality variable (three samples of size four each):

Machine	Measurements
#1	15	14	15	12
#2	18	16	20	16
#3	16	17	16	17

If the process is known to have a mean of 15 and a standard deviation of 3, what are the 3 upper and lower control limits for an x-Bar (Sample Mean) chart?