Breakfast Cereal Marketing, level 2 Inference

Transcription

1 Breakfast Cereal Marketing, level 2 Inference Problem: I wonder if the median sugar content of USA breakfast cereals (in grams) per serving marketed to children tends to be higher than all customers (general) using data from 2710 breakfast cereals sold in USA supermarkets (sourced 8/10/14). Variables investigated: sugar market sugar content of cereal (in grams) per serve as indicated on product packaging cereal was marketed mostly to children, or to all customers (general). Serving sizes varied across packaging, typically from 80 to 120 grams it is determined by the manufacturer. The data consists of 2710 breakfast cereals sold in USA supermarkets (sourced 8/10/14). Sugar Market 11 children 9 general 3 general 9 children 5 general Plan and data: For this investigation a simple random sampling method will be used. This method gives.. Using a simple random sampling method and generating random samples on nzgrapher and collecting a sample of 100 and 400 entries from a sample size of Checking the proportions of general cereal sugar content and children's cereal content in the sample to be a true representation proportionately of all the USA cereals from 2014 used in the survey. This will allow an investigation, and therefore make an inference on American cereals which have been used in this study. To explore the data and see if higher sugar levels (or contains more sugar per serving) are in children s cereals or not compared to cereals targeted to all other age groups (general). Using research, cereals for children contain more sugar as it provides extra energy and a better taste. 1 P a g e

2 Children usually prefer chocolate or sweet flavoured cereals as compared to sugar-less or healthy cereals such as normal cornflake. Following this, I expect to see children's breakfast cereal do tend to have a higher sugar content compared to the sugar content of general cereals. Include research The proportions in the USA data are Children = 35.8% General = 64.2% The 100 random sample proportion Children = 26% General = 74% The 400 random sample proportion Children = 38.8% General = 61.2% This random sample consisting of 100 pieces of data only has 26 individual pieces selected that of children data. Therefore only 26 cereals marketed to children have been chosen. This is a concern as it is stated there should be a minimum of 30 pieces of data in which to make a sound inference. Also the proportions of 26% for children s cereals and 74% of cereals marketed to the general USA population does not reflect the proportions of the whole data of USA cereals. A sample of 400 was also taken from the full data set so as to see the effect of the quadrupled sample size. By doing so the proportions in this sample are a lot closer to the actual proportions of the true cereal data set given. Thus showing a larger sample appears to better reflect the true proportions. 2 P a g e

3 This random sample of 100 American cereals: For children the sample is unimodal. If a sample is symmetric the mean and median are the same. In this sample the mean is 10.5 grams of sugar per serve and the median is grams. Therefore the children s sample is almost symmetrical however the cereals for general is skewed with a slightly longer tail to the upper values, mean is 5.46 grams and median of 4.5 grams. However, because this is a relatively small sample, the same skew might not be present in the breakfast cereals in the population. The median is a better measure of centre as it not affected by skewness or unusual values. There doesn t appear to be any unusual values in this sample. The median sugar content in cereals for children is 10.3 grams per serving, 5.8 grams higher than the cereal targeted to all other customers. The interquartile range (middle 50%) for the sugar content in cereals per serve for children, goes from 9 to 12 grams (a spread of 3 grams) compared to 3 to 9 grams for general (a spread of 6 grams). There is no overlap showing the middle 50% of the sample for the American children s cereals are higher than the general cereals. The median informal confidence for the sugar content in cereals per serve for children, goes from 9.6 to 11.3 grams (a spread of 1.7 grams) compared to 3.5 to 5.5 grams for cereal (a spread of 2 grams). The lower content for children is higher than general s upper content by 4.1 grams. Using median total sugar content in cereals is within 1.5 IQR grams of the sample median P a g e

4 For children the sample is unimodal. This random sample of 400 American cereals: If a sample is symmetric the mean and median are the same. In this sample the mean is 10.9 grams of sugar per serve and the median is 11 grams. Therefore the children s sample is almost symmetrical however the cereals for general is very slightly skewed with a longer tail to the upper values, mean is 5.44 grams and median of 5 grams. Once again the median is a better measure of centre as it very rarely affected by skewness or unusual values. There doesn t appear to be any unusual values in this sample. Although for the children s cereal there are a few values at 1 gram of sugar per serving. I wonder if this is an equivalent cereal to our weetbix. We are not told the names of the American cereals but it s good to see there are some with a lower sugar content making them healthier. I have researched American cereals and they could be Also there are cereals with 0 grams of sugar. I find this unusual as there are quite a few cereals in this category. [1] Shows these cereals to be oat or bran based and targeted towards diabetics. Unfortunately they need to be sweetened when served making the sugar content higher. The median sugar content in cereals for children is 11 grams per serving, 6 grams higher than the cereal targeted to all other customers. Children tend to like foods that look and taste exciting, unfortunately that often means they contain colouring and are sugary, [3] likens it to dessert for breakfast. The interquartile range (middle 50%) for the sugar content in cereals per serve for children, goes from 9 to 12 grams (a spread of 3 grams) compared to 3 to 8 grams for general (a spread of 5 grams). There is no overlap showing the middle 50% of the sample for the American children s cereals are higher than the general cereals. The median informal confidence for the sugar content in cereals per serve for children, goes from 10.6 to 11.4 grams (a spread of 0.8 grams) compared to 4.5 to 5.5 grams for cereal for general (a spread of 1 gram). 4 P a g e

5 The lower content for children is higher than general s upper content by 5.1 grams. Using median total sugar content in cereals is within 1.5 IQR grams of the sample median. 400 Comparing these random samples of American cereals: The median informal confidence for this random sample of 100 American cereals has a range of 2 grams per serve whereas the sample of 400 has a range of 0.8 grams. The length of the median informal confidence interval for the 400 sample is slightly less than half the 100 sample showing the interval has indeed halved. Thus showing a larger degree of accuracy for an inference. Sampling variation These samples appear to be representative sugar levels in American cereals and therefore is likely to be useful for generating an estimate of the population medians. I would expect that another sample of American cereals would give a similar distribution of measured sugar content, but with some variation. Taking a larger sample has reduced the size of the informal confidence intervals for the median sugar content per serve in American cereals. We are using the sample median to construct an interval in which we think the population median will be located. For any one single interval, we expect individual variation, but on average over all possible intervals, we expect 90% of them to include the true median of the sugar levels in American cereals. The true median for grams of sugar per serving in American cereals for the full data is 11 grams for children and 4 grams for general. Two more samples of 100 pieces of data have been taken to investigate the difference. I will compare these to the whole population of sugar levels in American cereals that were surveyed. If not why?... 5 P a g e

6 If a sample is symmetric the mean and median are the same. In both of these samples for children, the mean and median grams of sugar per serve are very close, therefore the data is quite symmetrical. However the cereals for general are skewed with a longer tail to the upper values, especially the third sample. The median informal confidence intervals for the second and third samples for the sugar content in cereals per serve for children, both contain the true median of 11 grams. The median informal confidence intervals for the second and third samples for the sugar content in cereals per serve for general, also contain the true median of 3 grams. The lower content for children is higher than general s upper content in all samples. Inference All of the samples taken appear to be representative of the true population of sugar content in American cereals marketed to children and all customers (general). Therefore is likely to be useful for generating an estimate of the population median. The median informal confidence for the sugar content in cereals per serve for children, goes from 10.6 to 11.4 grams compared to 4.5 to 5.5 grams for cereal for general. The lower content for children is higher than general s upper content by 5.1 grams 6 P a g e

7 I am fairly sure that, there is evidence, that for all American cereals surveyed, the median sugar content per serve is higher when targeted to children compared to general. This is because the median informal confidence intervals do not overlap. This matches with the research from [1] [2] and [3], which states a problem with sugar content in American cereals targeted to children. Evaluation A concern has been stated as it is a relatable factor of obesity in children. Unfortunately the age of the children group has not been stated. At what age are they no longer children? A child between the age of 5 and 12 uses up less sugar and carbohydrates than a teenager. The data was collated and shared with the public in 2014 and therefore could be out dated and therefore updated data could be collected. Also an investigation can be looking into the sugar content sugar of cereals in NZ compared to American cereals. Bibliography [1] found 23/6/16 [2] found 23/6/16 [3] found 23/6/16 7 P a g e