#27Refer to the data given for the change-of-majors study in

#27Refer to the data given for the change-of-majors study in the data file MAJORS. Consider gender and whether students changed majors as the two factors. Analyze the data for GPA, the college grade point average. Your analysis should include a table of sample sizes, means, and standard deviations; Normal quantile plots; a plot of the means; and a two-way ANOVA using sex and major as the factors. Write a short summary of your conclusions.obssexmajsatmsatvhsmhsshsegpa1116405308682.3521167060091072.083116004008873.214115704807762.345115105306881.461175061010991.437116504608962.48811720630101093.73911760500101093.810116406709652111164049010983.1612115203609872.7313117005207861.0714114905506861.821511640520101073.1216115502909742.2517116005201010102.93181171053010992.83191175067091093.120116204809992.872111630440101093.61221177072010752.752311610560101093.2624116405701010103.672511650480101093.32611660630101083.6227115704807882.5528116905509783.2529116705007782.21301166046010992.531116006308873.03321144732091081.9233115804706862.734116306309782.9635116005601010102.76361155056091093.437116305008872.4838117507601010103.8639114913919872.6240125505007873.7241125505007873.7242126305008783.543126305008783.544126305008783.545126904406772.8346126904406772.8347125404008653.0648125404008653.0649126404809101045012640480910104511252041081083.7521252041081083.753125594889742.8154125594889742.8155125905108681.9356125905108681.9357125905108681.9358125805801010103.759125805801010103.760126704409762.9661126704409762.9662126205909982.6463126205909982.6464126205909982.646512540470101083.096612540470101083.0967126205604343681262056043436912620560434370127705401010102.9771127705401010102.9772126205701010102.8173126205701010102.8174126205701010102.817512660560109103.327612660560109103.3277127105007843.478127105007843.479136103909661.8480135606906670.481136904609762.8882135904406592.778313530560710102.438413640500101062.6385135904708431.6686135595457782.1287134903706772.4688136704808971.598913720610101071.1490136405209770.6591135203807672.1292134804108972.3493134803906992.1194135304706781.3495136406309893.1496136905801010102.2597134703306562.3998134804606662.1599135405907660.75100135103805993.06101136904908882.44102135904807771.11103135803401010103.12104136505008782.171051353032065621061362043010661.881071372074010992.58108135904406662.1610913630500710102.51101370048010871.85111136204009982.95112135866976570.911131358667099102.67114137005009872.51115135505707751.79116135055186682.42117135152855770.58118215705701010102.76119215705701010102.76120215805409993.35121215805409993.35122215805409993.351232156053010983.81242156053010983.81252165057099102.381262165057099102.3812721440430101092.5812821440430101092.58129215707501010103.18130215707501010103.18131214765768872.87132214765768872.87133216807008983.16134216807008983.16135214904809893.07136214904809893.071372159049010893.681382159049010893.6813921590580109103.3414021590580109103.341412165049010881.931422165049010881.93143214805209592.43144214805209592.43145216704901010103.28146216704901010103.28147217106001010103.66148217106001010103.66149215705707682.29150215705707682.29151215404606562.19152215404606562.19153216205101010103.06154216205101010103.06155216304708683.41156216304708683.411572263070099103.141582263070099103.141592263070099103.141602263070099103.141612261046010882.851622261046010882.851632261046010882.8516422720680101093.4716522720680101093.4716622720680101093.4716722720680101093.4716822640590101093.4416922640590101093.4417022640590101093.4417122640590101093.44172226505001010103.9173226505001010103.9174226505001010103.9175226505001010103.9176226404309993.65177226404309993.65178226404309993.65179226404309993.65180227404609891.32181227404609891.32182227404609891.32183226006601010103.23184226006601010103.23185226006601010103.2318622650430109102.8618722650430109102.8618822650430109102.861892251044089102.511902251044089102.511912251044089102.51192225505108982.86193225505108982.86194225505108982.86195225505108982.86196236305609793.3319723710470101083.6919823417518910102.5719923600600810102.28200234604604771.6201233002902462202235604807671.692032359042091093.062042355044091082.622052355066071090.392062365035010992.44207236105209983.46208235304808792.372092355045010992.8210235604205482.14211234303307782.452122349040097102.712132369051099102.93214235704807692.53215234704208692.69216234703308881.942172351036010893218234504609782.0921923490410109103.342202353051069102.25221235804901010104222235804906572.72223236204209782.61224235003901010103.39225235905808683.64226236206008791.82272352057099101.52228234804806993.422923640560109103.32230236004409762.07231235104807790.85232233563507971.86233236304705472.59234235594889892.28#28Search the Internet or your library to find a study that is interesting to you and uses a two-way ANOVA to analyze data. First describe the question or questions of interest and then give the details of how ANOVA was used to provide answers. Be sure to include how the study authors examined the assumptions for the analysis. Evaluate how well the authors used ANOVA in this study. If your evaluation finds the analysis deficient, make suggestions for how it could be improved.#29A study of undergraduate computer science students examined changes in major after the first year. The study examined the fates of 256 students who enrolled as first-year students in the same fall semester. The students were classified according to gender and their declared major at the beginning of the second year. For convenience we use the labels CS for computer science majors, EO for engineering and other science majors, and O for other majors. The explanatory variables included several high school grade summaries coded as 10 = A, 9 = A-, etc. Here are the mean high school mathematics grades for these students.Major Gender CS EO O Males 8.68 8.35 7.65 Females 9.11 9.36 8.04 Describe the main effects and interaction.