In order to assess rates of faulty installation for home solar panel arrays, a sample of homes with recently installed arrays was examined
by expert assessors and each array was graded as either "unsafe", "sub-standard" or "acceptable". The table below shows the breakdown of assessments by geographic location of the installed array:Major Metropolitan, Suburban and Rural.We first wish to assess whether there are differences in the assessment patterns for the three geographic regions. To undertake such an analysis, we should employ:

a. Test of independence using a chi-squared distribution
b. Test of difference in proportions using a standard normal distribution
c. Test of difference in means using a t-distribution
d. 9 separate tests of a single proportion, one for each table cell, using a normal distribution calculate the value of the appropriate test
statistic

In carrying out the test of Question 1, what degrees of freedom should be used?
In carrying out the test of Question 1, the p-value turns out to be 0.23. This means:
a. We have proven there is no difference between assessment patterns in the three locations
b. There is a highly statistically significant difference between the observed assessment patterns from the three locations
c. There is no statistically significant difference between the observed assessment patterns from the three locations
d. There is a 23% chance that a difference exists between the true assessment patterns from the three locations
Suppose we continued gathering data and increased our sample size ten-fold such that:In this case, the value of the appropriate test statistic would be 56.133 and the associated p-value would 1.9 x 10-11. In this case
a. We have proven there is no difference between assessment patterns in the three locations
b. There is a highly statistically significant difference between the observed assessment patterns from the three locations
c. There is no statistically significant difference between the observed assessment patterns from the three locations
d. There is a 1.9 x 10-9% chance that a difference exists between the true assessment patterns from the three locationsFor the dataset in

Question 5, which has a much larger sample size, care must be taken in interpreting the outcome of our test because:
a. The increased power of the test means we will be able to detect statistically significant differences which may not be of practical  significance
b. The p-value changes meaning as the sample size increases
c. The Type I error rate of the test changes as the sample size increasesd. The appropriate test statistic changes as the sample size increases