Example 1.3 The marketing research case: Rating a bottle design Please define th
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Example 1.3 The marketing research case: Rating a bottle design
Please define the element for the example? What are the variables?
Based on the table(s) or figure(S) from the example, please determine whether the data set is quantitative data or qualitative (i.e. categorical) data. Please further define if it is ratio, interval, ordinal, or nominative variable.
Based on the table(s) or figure(S) from the example, please determine whether the data set is cross-sectional data or time-series data.
Based on the example, please determine where the data comes from (i.e. “existing sources” or “experimental and observational studies”).
Based on the example, please determine if the example is a census study. If not, what are the population and sample size for the example?
Based on the example, is it the case of descriptive statistics or a study of statistical inference?
EXAMPLE 1.3 The Marketing Research Case: Rating a Bottle Design
Part 1: Rating a Bottle Design The design of a package or bottle can have an important effect on a company’s bottom line. In this case a brand group wishes to research consumer reaction to a new bottle design for a popular soft drink. Because it is impossible to show the new bottle design to “all consumers,” the brand group will use the mall intercept method to select a sample of 60 consumers. On a particular Saturday, the brand group will choose a shopping mall and a sampling time so that shoppers at the mall during the sampling time are a representative cross-section of all consumers. Then, shoppers will be intercepted as they walk past a designated location, will be shown the new bottle, and will be asked to rate the bottle image. For each consumer interviewed, a bottle image composite score will be found by adding the consumer’s numerical responses to the five questions shown in Figure 1.4. It follows that the minimum possible bottle image composite score is 5 (resulting from a response of 1 on all five questions) and the maximum possible bottle image composite score is 35 (resulting from a response of 7 on all five questions). Furthermore, experience has shown that the smallest acceptable bottle image composite score for a successful bottle design is 25.
Part 2: Selecting an Approximately Random Sample Because it is not possible to list and number all of the shoppers who will be at the mall on this Saturday, we cannot select a random sample of these shoppers. However, we can select an approximately random sample of these shoppers. To see one way to do this, note that there are 6 ten-minute intervals during each hour, and thus there are 60 ten-minute intervals during the 10-hour period from 10 A.M. to 8 P.M.—the time when the shopping mall is open. Therefore, one way to select an approximately random sample is to choose a particular location at the mall that most shoppers will walk by and then randomly select—at the beginning of each ten-minute period—one of the first shoppers who walks by the location. Here, although we could randomly select one person from any reasonable number of shoppers who walk by, we will (arbitrarily) randomly select one of the first five shoppers who walk by. For example, starting in the upper left-hand corner of Table 1.4 and proceeding down the first column, note that the first three random numbers between 1 and 5 are 3, 5, and 1. This implies that (1) at 10 A.M. we would select the 3rd customer who walks by; (2) at 10:10 A.M. we would select the 5th shopper who walks by; (3) at 10:20 A.M. we would select the 1st customer who walks by, and so forth. Furthermore, assume that the composite score ratings of the new bottle design that would be given by all shoppers at the mall on the Saturday are representative of the composite score ratings that would be given by all possible consumers. It then follows that the composite score ratings given by the 60 sampled shoppers can be regarded as an approximately random sample that can be used to make statistical inferences about the population of all possible consumer composite score ratings.
Part 3: The Approximately Random Sample and Inference When the brand group uses the mall intercept method to interview a sample of 60 shoppers at a mall on a particular Saturday, the 60 bottle image composite scores in Table 1.6 are obtained. Because these scores
FIGURE 1.4 The Bottle Design Survey Instrument
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vary from a minimum of 20 to a maximum of 35, we might infer that most consumers would rate the new bottle design between 20 and 35. Furthermore, 57 of the 60 composite scores are at least 25. Therefore, we might estimate that a proportion of 57/60 5 .95 (that is, 95 percent) of all consumers would give the bottle design a composite score of at least 25. In future chapters we will further analyze the composite scores.
34 33 33 29 26 33 28 25 32 33 32 25 27 33 22 27 32 33 32 29 24 30 20 34 31 32 30 35 33 31 32 28 30 31 31 33 29 27 34 31 31 28 33 31 32 28 26 29 32 34 32 30 34 32 30 30 32 31 29 33 CEXAMPLE 1.3 The Marketing Research Case: Rating a Bottie Design Part 1: Rating a Bottle Design The deaign of a package or bottle can hae an important effect on a company's bottom line. In this case a brand proup wishes to research consumer reaction to a new bottle design for a popular soft drink. Because it is impossible to show the new battle des n to all co somers the b and group m use the ma m ercepr merho to select n sample of 60 consumers On a parter lar Sar rda the brand group will choose a shopp ng mall and a sampling time so that shoppers at the ma dnring e sampling time are represe tative cross see son of a consumers hen s o opers wil be intercepted aa they walk pasn des nated ocation m be shon n the new bottle and wil be ?ted to m e the battle image or each cons er in er iewed a bon e image compos te score be found by adding the consmer's numerical responses to the five questiona shown in Figure4. I follows that the minimum possible botle image composite score is (resulting from a reponse of 1 on all fire questions) and the maximum possible botle image composite score is 35 (resulting from a response of 7 on all fve questioes) Furthermore, experience has shown that the smallest acceptable bottle image composite score for asccesful botle design is 25 Part 2: Selecting an Approximately Random Sample Becuse it is not possible to list and number all of the shoppers who will be at the mall on this Satarday, we cannct select a random sample of these shoppers Howeer, we can select an approxwarely random sample ofthese shoppers To see one way to do us note hat there are 6 en minute inter als dring each hour and thas there are 60 ten minute terals durin?the 10 hour persod om 10 A3L to 8 pM he time when tse shoppanz mall ss open Therefore one way to select an approxi ately random sample is to choose a particlar location at the mall that most shoppers will walil by and then randomly select a: the beginning of each ten-minute period one of the first skoppers who wallks by the location. Here, although we could randomly select os person from any reasonable nmber of shoppers who walk by, we will (arbitrarily) randomly select one of the first five shoppers who wall by. For example, starting in the upper left-hand corner of Table 4 and proceeding domn the first column, note that the first three random numbers between 1 and 5 are 3, 5, and 1. This implies that (I) at 10 AM we would select the 3rd customer who walks by(2) at 10:10 AL we woald select the Stlh shopper who wallks by: (3) at 10:20 AM we wauld select the 1st customer who walks by and so forth. Furthermore assume that the composite score ratings of the new bottle design that woald be given by all shoppers at the mall on the Saturday are representative of the compasite score ratings that would be given by all poasible consumers. It then foellows that the composite score ratings given by the 60 sampled shoppers can be regarded as an approximately randon sample that can be used to make statistical inferences about the population of all possible consumer composite score ratings Part 3: The Approximately Random Sample and Inference When the brand group uses the mall intercept method to interview a sample of 60 shoppers at a mall on a partieular Saturday, the 60 bottle image composite scores in Table 1.6 are abtained. Because these FICURE 1.4 The Bottle Design Survey Instrument Please circle the response that most accurately describes whether you agree or disagree with each state- ment about the bottle you have examined Strongly Disagree Statement The size of this bottle is convenient. The contoured shape of this bottle is easy to handle. The label on this bottle is easy to read This bottle is easy to open Based on its overall appeal, I like this bottle design. 1 2 345 6 7 4 5 14 TABLE 1.6 A Sample of Bottle Design Ratings (Composite Scores for a Sample of 60 Shoppers) OS Design 32 24 31 32 31 32 26 32Explanation / Answer
Here the variable is the responses of 5 questions for which the responses on a scale of 1 to 7 are recorded.
Here the responses on a scale of 1-7 is ordinal scale as it gives an idea of order of choices of respondents.
As we know that cross sectional data is a type of data collected by observing many subjects at tge same point of time or without regard to differences in time.
And time series data is a series of data points indexed in time order.
So obviously the given data composite score is cross sectional data.
Here the data are collected by observing the observers by taking their responses. So it comes from observational study.
No it is not census study as we are studying responses of 60 shoppers only. So sample size is 60 and population is all available consumers of the soft drink
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