### BEA140 Quantitative Methods Make Up Assignment

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Make Up Assignment (optional)BEA140 Quantitative MethodsSemester 2, 2014Due 4:00 pm, 17 OctoberTotal Marks Available: 50Contribution to final mark 5% (see page 4)Section A: Attempt Question 1Question 1One of the key measures of the success of TV“infomercial”advertising is the amount of information that viewers canrecall about the advertised product.The marketers of a new fat free cooking system have had three infomercials developed:A spokesperson style advertisement featuring a celebrity,A product demonstration style advertisement showing the product being used,A testimonial style advertisement, featuring satisfied users.They are wondering whether they are equally suited to day time television, in particular whether or not there issignificant variation in the level of product recall associated with the three advertisements. Their researchers compilethree random samples of day time television viewers – one sample for each advertisement. Each sample has 12viewers. The viewers are shown their particular advertisement, and then are tested on their recall. Their recall scores(out of 100) appear in the table below.SpokespersonDemonstrationTestimonial457062685873497546515448454959497256377571485755297064475164667448646872aPresentthe data as a fully labelled“multi vari”chart of the form used on page two of the ANOVA handout. (NBHand drawn charts are acceptable. Novice users of Excel may find it easier to draw the chart by hand.)[7 marks]bBeing careful to state any assumptions that you may need to make,testat the=0.10 level, whether productrecall varies across the infomercials.Stateyour conclusions clearly.Include a referenceciting where you obtainedthe critical value.[8+1+1=10 marks]cSummariseyour calculations using an ANOVA summary table.[6 marks]dThe Marketing manager claims that this exercise proves that product demonstration causes increased Recall.Explainwhether the manager’s claim is correct.[2 marks][Total: 25 marks]1

Section B: Attempt Question 2Question 2The World Fair Monorail Company (WFMC) operates five monorail circuits, one in each of Shelbyville, Brockway andOgdenville, and two in Springfield (an older monorail and a newer one). Each month, as part of an ongoing customerservice monitor, a random selection of travellers are interviewed about their most recent monorail experience. One ofthe questions asks the traveller to rate the monorail’s cleanliness. The most recent month’s results appear in the tablebelow.CircuitCleanlinessShelbyvilleBrockwayOgdenvilleOld SpringfieldNewSpringfieldTOTALSatisfactory282943227129Unsatisfactory11344123TOTAL393247268152The management of WFMC wish to understand whether all of their monorails are performing equally well withrespect to perceived cleanliness. (That is, whether cleanliness is independent of circuit.)aBeing careful tostate your conclusions, and using a level of significance of= 10%,testwhetherperception ofcleanlinessis independent ofcircuit.[21 marks]bExplainthe difference between a type 1 and type 2 error. Use this problem to provide examples.[4 marks][Total: 25 marks]SolutionsAnswer 1.aThe“multi vari”chart of the form used on page two of the ANOVA handout is shown below:TestimonialDemonstrationSpokesperson807060504030DataIndividualValuePlotofSpokesperson,Demonstration,TestimonialAccording to the above multi vari chart, the mean of the spokesperon is 49.83, which indicate the meanstyleadvertisement featuring a celebrity. Thethe mean of the demonstration is 64.42, which indicate the meanstyle2

advertisement showing the product being used. Thethe mean of the testimonial is 59.83, which indicate thestyleadvertisement, featuring satisfied users.Answer 1.bConsider the provided details of 12 viewers of each sample who have been selected for three advertisements. Thelevel of product associated with the three advertisements, a spokesperson style advertisement featuring a celebrity, aproduct demonstration style advertisement showing the product being used and a testimonial style advertisement,featuring satisfied users. So there are three samples with three different conditions. So, the samples can be considerdas independent. The condition of the independent level is also called a level or a treatment. And the differenceproduced by the independent variable is called a treatment effect. The independent variables are called as betweensubject factor. Hence, to heck the differences between sample means the one-way ANOVA will be used.Assumptions for the one-way ANOVA are given as below:1. Dependent variable should be measured at the interval or ratio level (Continuous).2. Independent variable should be measured at the two or more categories.3. There is no relationship between the observations of each group in independent variable.4. There are no significant outliers.5. Dependent variable should be normally distributed for each category if independent variable.6. There needs of homogeneity of variance, so the Levene’s test will be applied for homogeneity of variance.Consider the null and alternate hypothesis to test the claim, as given below:0123:HAgainst the alternative hypothesis as shown below:1:ijHHere,1,2and3are the means of,a spokesperson style advertisement featuring a celebrity, a productdemonstration style advertisement showing the product being used and a testimonial style advertisement featuringsatisfied usersrepectively. Consider the level of significance for the test as0.05.Now compute the test statistics as given below:SpokespersonDemonstrationTestimonialTotal457062685873497546515448454959497256377571485755297064475164667448646872598X773X718X208912n12n12n36N5981249.83XXn7731264.416XXn7181259.83XXn231252X250865X243956X1260733

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