Q$1.$ Consider the following computer output for an experiment.

Source DF SS MS F P$-$value

Factor $5????$

Error $?27\mathrm{.}28?$

Total $2966\mathrm{.}44$

$($a$)$ How many replicates did the experimenter use?

$($b$)$ Fill in the missing information in the ANOVA table.

$($c$)$ Compute an estimate for ${}^2$

Q$2.$ An article in Fuel Processing Technology described an experiment to investigate the effect of potassium hydroxide in synthesis of biodiesel. It is suspected that potassium hydroxide $($PH$)$ is related to fatty acid methyl esters $($FAME$)$ which are key elements in biodiesel. Three levels of PH concentration were used, and six replicates were run in a random order. Data are shown in the following table:

PH concentration$($wt$.\%)$ FAME concentration $($wt$.\%)$

Observations

$123456$ Total Average

$0\mathrm{.}684\mathrm{.}384\mathrm{.}586\mathrm{.}586\mathrm{.}786\mathrm{.}986\mathrm{.}9$

$0\mathrm{.}989\mathrm{.}389\mathrm{.}488\mathrm{.}588\mathrm{.}789\mathrm{.}289\mathrm{.}3$

$1\mathrm{.}290\mathrm{.}290\mathrm{.}388\mathrm{.}989\mathrm{.}290\mathrm{.}790\mathrm{.}9$

Solve Manually. a and b$,$ using $=0\mathrm{.}05$

a$.$ Construct the analysis of variance. Are there any differences in PH concentrations at$?$ Calculate the P$-$value.

b$.$ Use the LSD for multile comparison to compare between PH concentrations factor $($given it is significant$)$

c$.$ Solve a and b using Minitab $,$ using $=0\mathrm{.}05$