Question

Solve these problems using R and report the results in a single PDF. The R code should be submitted separately 1. A microbiologist is investigating the growth of algae in acetic acid. She suspects that the pH level, temperature, and size of vessel in which the algae is grown influences the growth of algae. She decided to use a 5 × 5 Graeco-Latin square design to isolate the variations due to other sources. The Greek letters represent temperature at five levels, the columns represent five settings of pH, rows represent the vessels, while the algae types are represented by the Latin letters. The responses as well as the design are shown in the table below. The observations are the number of molds of the algae obtained after 3 days of growth Columns 3 Rows 1 2 4 Вф 55 C 43 Du, 38 A 23 E 71 (a) Construct the appropriate ANOVA table for the above design (b) Formally test to determine if temperature affects the growth. (c) Formally test to determine if algae type affects the growth (d) Formally test to determine if pH affects the growth (e) Formally test to determine if the size of vessel affects the growth i. If it does, what temperatures result in significantly different growth? i. If it does, what algae types result in significantly different growth? i. If it does, what pH levels result in significantly different growth? i. If it does, what vessel sizes produce significantly different results?

Answer 1

a) 8oth pressue a and temperatune & are Srn feant the nteracuon s that ANovA fox Selected Focota) Model Analysts of vartable table CParHal Sum of square SouTce Sum o DF SquoveS Prob>F Model Square 0. 0026 o.3 aI.Sa o 0004 0I5 847o o08 S 3 0-77 2 o.069 Rest dua Lack offt toure 0 017 4300 0.00 O 018 a 0 018 error The Mode F-value of 8.00 fmplres the Modej 's Stq n?frcant rhere ↑s only a 0,267. a model Fvalue ths larje could be occurs due to nofse Change that

values ot prob>F less than o.os fndicat model berms are Srgnffcant. 1n hts case A,B srntfcant model te ms.Values redtex than o 100 indtcate the model terms are not Srgni Hcant If there are many Stgntftcant model terms model geduction may fr por. our model b). The Residual plot Shous no setes devtaHon from the assumplon Residuai vs predicted 0 IS 0.0 乙 0IS 007s 0.01s os Restdual vs pressure Residual Vs Temperature 0.07 O IS 3