Stats Homework

Bill Seyfarth

Homework 7

1. No. t* should not equal t but they should be relatively close to one another. The tn-1 distribution shows from -t* to t*, the area under the distribution curve equals the confidence interval.

1. The null hypothesis is that the process is in control. The alternative hypothesis is that the Process if not in control.
2. True positive means that the process is not in control. A true negative means that the process is in control. A false positive means the process is in control. False negative means the process is not in control.
3. More conservative bounds are used here because if a process is in control you don’t want to be flagging it as out of control 1 out of 20 times. Which, would happen if we used a 2σ or .05 approach. 2 sigma approach will give you more false positives.
4. No process is 100% perfect. Even though the confidence interval is 99.7%, there is still room for variations. There shouldn’t be a surprise that there is a variation that leads to the .3% die to systematic change or statistical noise.

1. No. Because if the median is larger than the mean, it would be skewed to the left. The mean and median should be equal to achieve normal distribution.
2. No. They will not be independent of one another. More dependent on seasonal changes. One days weather has an effect on the next days.
3. The numbers will definitely vary because more undergrads will be at the bars towards the end of the week then at the beginning due to class and homework. In addition, many are away on break during the summer so the numbers will not be consistent throughout each month. You expect more to be out and about when the weather is nice as well so more sales would likely occur in the Fall and Spring months.

4.

a)

[pic 1]

We removed observation 33 because it was an outlier. Phase 2 is now the next step now that everything is within the UCL and LCL and there are 0 violating runs.

b)

 [pic 2]

This process is not in control because there is one violating run between 83 and 87 which means 7 groups showed up below the CL line.

5.

a)

Histogram:

[pic 3]

qqnorm:

                  [pic 4]

qqline:

[pic 5]

The data is skewed to the right when looking at the histogram so the normality assumption does not hold. The majority of the data is to the right of the mean rather than evenly distributed. The qq plot shows the data rising to the right which also shows it is not normally distributed.