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BEA140 Quantitative Methods Make Up Assignment

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Added on  2020-05-04

BEA140 Quantitative Methods Make Up Assignment

   Added on 2020-05-04

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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 can recall 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 is significant variation in the level of product recall associated with the three advertisements. Their researchers compile three random samples of day time television viewers – one sample for each advertisement. Each sample has 12 viewers. 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.SpokespersonDemonstrationTestimonial457062685873497546515448454959497256377571485755297064475164667448646872aPresent the data as a fully labelled “multi vari” chart of the form used on page two of the ANOVA handout. (NB Hand 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, test at the =0.10 level, whether product recall varies across the infomercials. State your conclusions clearly. Include a reference citing where you obtained the critical value.[8+1+1=10 marks]cSummarise your calculations using an ANOVA summary table.[6 marks]dThe Marketing manager claims that this exercise proves that product demonstration causes increased Recall. Explain whether the manager’s claim is correct.[2 marks][Total: 25 marks]1
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Section B: Attempt Question 2Question 2The World Fair Monorail Company (WFMC) operates five monorail circuits, one in each of Shelbyville, Brockway and Ogdenville, and two in Springfield (an older monorail and a newer one). Each month, as part of an ongoing customer service 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 with respect to perceived cleanliness. (That is, whether cleanliness is independent of circuit.)aBeing careful to state your conclusions, and using a level of significance of = 10%, test whether perception of cleanliness is independent of circuit.[21 marks]bExplain the 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 mean style advertisement featuring a celebrity. The the mean of the demonstration is 64.42, which indicate the mean style 2
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advertisement showing the product being used. The the mean of the testimonial is 59.83, which indicate the style advertisement, 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:HAgainst the alternative hypothesis as shown below:1:ijHHere, 1, 2and 3are 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 users repectively. Consider the level of significance for the test as 0.05.Now compute the test statistics as given below:SpokespersonDemonstrationTestimonialTotal457062685873497546515448454959497256377571485755297064475164667448646872598X773X718X208912n12n12n36N5981249.83XXn7731264.416XXn7181259.83XXn231252X250865X243956X1260733
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