Please answer part a) through part d) of the question below.Thank you.
Question 3
A tobacco refinery has four methods of measuring pH. To testthe
four methods, a supervisor randomly assigns each of 32tobacco
samples with known pH to one of the four methods, so thateach
method is applied to exactly eight samples. The differencebetween
measured pH and the known pH is recorded, and the data isbelow.
| Method | Sample | Response |
| A | 1 | -0.307 |
| A | 2 | -0.294 |
| A | 3 | 0.009 |
| A | 4 | -0.051 |
| A | 5 | -0.136 |
| A | 6 | -0.324 |
| A | 7 | -0.324 |
| A | 8 | -0.164 |
| B | 1 | -0.110 |
| B | 2 | 0.125 |
| B | 3 | -0.013 |
| B | 4 | 0.082 |
| B | 5 | 0.091 |
| B | 6 | 0.459 |
| B | 7 | 0.259 |
| B | 8 | 0.351 |
| C | 1 | 0.137 |
| C | 2 | -0.063 |
| C | 3 | 0.24 |
| C | 4 | -0.05 |
| C | 5 | 0.318 |
| C | 6 | 0.154 |
| C | 7 | 0.099 |
| C | 8 | 0.124 |
| D | 1 | -0.042 |
| D | 2 | 0.69 |
| D | 3 | 0.201 |
| D | 4 | 0.166 |
| D | 5 | 0.219 |
| D | 6 | 0.407 |
| D | 7 | 0.505 |
| D | 8 | 0.311 |
a) Use R to calculate the means and standarddeviations for the four
methods. Based only on these numbers, do the mean pHdifferences
seem to differ across the methods? Explain.
b) Do the ANOVA conditions hold? Be sure toinclude your R code,
output, appropriate graphs (boxplots, dotplots), andexplanations.
c) Regardless of your answer to (b), run ANOVAwith R. Set-up your
null and alternative hypotheses; provide your test statistic,p-value,
and conclusion.
d) Use the Bonferroni adjustment to make aconfidence interval for
each of the 6 differences between treatment means, using an
experiment-wise confidence level of 95%.
