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2.A national cereal company Is planning to introduce new children brealfast cereal and wants tO slIvey people about their reaction [0 the proposed bratd uame a) Des...

Question

2.A national cereal company Is planning to introduce new children brealfast cereal and wants tO slIvey people about their reaction [0 the proposed bratd uame a) Describe how you would design each of the following samples_ 1) A systematic sample [2 marks] ii) A stralified sample [2 marks] Iii) A cOnVenience sample [2 marks] What are tle advantages ad disadvantages of sampling only children? [? marks]

2.A national cereal company Is planning to introduce new children brealfast cereal and wants tO slIvey people about their reaction [0 the proposed bratd uame a) Describe how you would design each of the following samples_ 1) A systematic sample [2 marks] ii) A stralified sample [2 marks] Iii) A cOnVenience sample [2 marks] What are tle advantages ad disadvantages of sampling only children? [? marks]



Answers

Each sampling method suffers from a form of bias. Identify the bias, tell how the sample statistic might differ significantly from the population parameter, and (writing to learn) suggest how the problem might be corrected.

To assess consumer response to its new cereal flavor, a cereal company passes out free samples at a local mall and offers shoppers a $\$ 5.00$ gift certificate if they will fill out a brief form evaluating the new product. They find that 94$\%$ of the respondents like the new flavor.

So looking at the dark plots first, let's take a look at the top shelf. So in the top shelf you see that there's this cluster off high sugar content and the frequency off those Israeli high. Whereas when you come down here on the bottom shelf, that cluster is totally missing. So when you actually look at the dark cloud product, then I would say no. The data does not support be clean, does not support weekly. And why do I say that is because of the difference in these two clusters?

So in this question, there's this claim made by the critics off supermarkets. The claim is that the poor trickery kids serials on your shelves where the kids can see them. And the question is, does the data support that claim? And looking at the data right here, I see there's a whole bunch off sugary cereals which are on the middle shelf, which is, in view off students, young kids, eyesight. So yes, he did. I don't support the claim and the evidence. It's from the high sugar content serials on the middle shelf, which is at kids high, high level.

We go back to question 35 b and we see that our answer for the standard deviation waas zero point 01 four four 052 Okay, so the question is, um if we want to get half of that standard deviation Well, then what? What our sample size have to be. So I'm gonna write the new standard deviation, which will be the old number divided by two. So that's what we go on. The standard deviation to be on our equation for standard deviation is P. Times one minus p over. End P. Back in question 35 B was zero 0.7 one minus p, with therefore be 0.3 and we're going to have a new end. So all we have to do now is solve this equation. How I would solve this equation is I would divide by two first to simplify the left side. That's gonna give me five point 18 seven seven four times 10 to the negative fifth power. So I squared both sides. So on the right side, I'm gonna have 0.7 time 0.3. Come on, over end. Next thing I'm gonna do is. I'm gonna take the reciprocal of both sides. Gonna flip it over. So the reciprocal of 5.18774 times 10 to the negative. Fifth power is 19,000 276.2 and the reciprocal the right side is an over 0.7 times 0.3. Yeah. Okay, Now all that's left is I'm gonna multiply by 7/10 and by 3/10 on both sides of the equation, and that gives me and equals 4000 48 and that is our new sample size.

Hi. So today we're looking at comparing the sugar content off cereals I would be given hissed, aground and sandbox almost close to work with. So the first question is asking us about the range. Now it's really hard to work out the range from history because you have this sort of bucket effects where any values between the low about in the upper bound fall into this book it and so we can't know where the values came from. So every fit, every value in this box could be a zero, and every value could be attending. We would have no way of knowing. And so I'm gonna use my box of despots to estimate the range. So we've got no allies that have been highlighted, and so we can use this top value to estimate the proper value by range. And that's coming in about 60 halfway between these two points. When we look at the lower end, this value here is coming around zero or where I'd expect there to be based on the scale how that no serial realistically has exactly zero sugar content. And so I'm going around that to be one for the sake of realism in this question, and so we expect the range to be 60 minus one. So about 59 is an estimate. The range, based on data that's know perfectly easy to find an accurate range, were the last to describe the shape on. We can use the history wanted. It's really easily as we can see, you've got to clear distinct peaks. And so we've got a by mail distribution going on that follows this sort of double curve thing that's going on. Question three is asking about why this might be. And as we conceive in the boxing with plots, there's two very separate sets of data that are targeted at adults and talk to the Children. And he's a really split on between, you know, down the middle. And so we would expect the the cereals from this peak appears in this sort of mode to be talked to the adults and zeros from this peak to be talked to the Children and similarly, uh, some zeros are targeted, you know, specifically as healthy low sugar cereals, which is bran flakes or fruit and fibre. Where is some cereals are definitely not talking that way, and I talked it because they have lots of sugar and they taste really good. And so you have a really clear distinction between these two camps rather than just we would you know, you wouldn't expect to see the same number of boxes through all these percentages. So part forwards asking us whether all Children cereals are hiring sugar than adults cereals. And so what we can see here is that even the lowest number, the minimum of the Children's target group, is above the maximum value of adults on. So what it tells us is that, yeah, every Children cereal is higher to content than every adult cereal, which is a little bit crazy. But we don't often see that in comparing two data sets so related. Yeah, often as some sort of overlap and questions. I was asking which group of cereals varies more digital content and again, we look at our books on with quotes to wait this out and we can see from the Q R for me in school, tell range. I'm from the general range within each section, a good idea of the spread. So we look at the Children's. There's a quite compact into court, our range going on here on as a fairly short set of whiskers. Whereas for the adults, we have a much wider inter quartile range. Just estimating off this graph. This is gonna be about 10. Whereas this one only looks to be about five. And again we have quite a tall whisker. And so from this fact, and especially from the difference in whipped of the inter quartile range, we would say that the adults cereals very more widely into the content, which again makes sense considering the general pitch off Children cereals that they are for healthy and tasty. Whereas there is quite a wide range of adult cereals all the way from your most healthy zero sugar ones to head, he's a pretty good. Maybe they hope it sugarless don't are gonna be the worst. And so it makes sense that they'd be a bit more than that read when we think about it.


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