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In a study of the effects of television advertising, investigators showed television program that included advertising for the new iPad Pro: The same commercial was...

Question

In a study of the effects of television advertising, investigators showed television program that included advertising for the new iPad Pro: The same commercial was shown twice during the program: Some subjects saw 30 minute program, with two 30-second commercials: The others saw 20 minute program; with two 60-second commercials- After viewing all of the subjects answered questions about their recall of the ad,their

In a study of the effects of television advertising, investigators showed television program that included advertising for the new iPad Pro: The same commercial was shown twice during the program: Some subjects saw 30 minute program, with two 30-second commercials: The others saw 20 minute program; with two 60-second commercials- After viewing all of the subjects answered questions about their recall of the ad,their



Answers

Advertising The effectiveness of a television commercial depends on how many times a viewer watches it. After some experiments an advertising agency found that if the effectiveness $E$ is measured on a scale of 0 to $10,$ then
$$E(n)=\frac{2}{3} n-\frac{1}{90} n^{2}$$
where $n$ is the number of times a viewer watches a given commercial. For a commercial to have maximum effectiveness, how many times should a viewer watch it?

This question asked us for commercial to have maximum effectiveness. How many times must be watched by a viewer? What we know is that are a is essentially negative 1/90. We're looking at the similar quadratic form that we've used for the all these problems in the section R B is two divided by three. Therefore, finding the quadratic using the formula negative be over to a listed in the textbook recon plug in or be divided by two times or a negative negative temples and becomes positive. 30. This is how many times, if you are

In this example, we're looking at the difference an ad we call time between shows with sexual content, violent content as well as neutral content. So when our first question, we've been told that they ran the numbers for the difference and add recall between sexual content and violent content, and they found a P value for the difference in these two means to be 20.136 So from this value can we say that there is a different? It's no So the reason being, we usually want at least 90% confidence before we say that their statistical significance. Of course it's better if it's 95% or 99% but at least 90% is kind of the cut off. So for a 90% confidence that it's statistically significant, we would need an Alfa value of one minus the dust. More form of that. So this is our Alfa and we would need RPI value to be smaller than Alfa in order for it to be significant. So, in other words, 0.136 would have to be smaller than point 10 on, and it is not so. We cannot say that there's a statistically significant difference between the means of the ad recall for sexual content and violent content. Now, if we were going to do this comparison between neutral on sexual content, you're going to want to run these numbers and your statistical software. All right, so we need a hypothesis. The hypothesis, of course, is that there is no difference at all. We always want them. No hypothesis. So the mean for the sexual minus the mean for the neutral. If there was no difference at all, so imagine it was 10 and 10 would be zero. That's are null hypothesis. And then our alternate hypothesis is that, of course, it does not equal zero. So if we were to run this data and our software comparing these two means we would come up with the following statistics. We would have a T of negative 6.8 with degrees of freedom of to 13.99 and a P value of five points five times 10 to the negative night. So this you can see there's a huge difference between this p value and the P value we've found when comparing the, um, sexual to the violent content, right? So neutral to sexual has a very, very, very small key value. So we can say with very high certainty that there is in fact, a difference on the way. I'm sure you've heard. This phrase is that we can, with the small key value, reject the null hypothesis. So in other words, because I got scrolled down here. So in other words, we can suggest that the ad recall between shows with sexual and neutral is in fact, different. Those with neutral content had ah higher on operated. Um, recall.

All right, so we got some commercials here. We've got some 12th commercials, some 22nd commercials and some 42nd commercials. But together they have the last two minutes, which is 120 seconds. They cost money. So we have $100 commercials, $180 commercials for $320 commercials. And the money total is 1016th. There's six commercials, so x plus y plus Z equals six and there are twice as many tens as there are forties. So X equals two z can also be part of our problem. So to solve our system, we're gonna put Cem make Pehrson, um, equations up. I'm gonna co a pair of the first and the last. That is my first step. So I'm gonna take X plus 21. I'm sorry. 10 x plus 20 y plus 40 z equals 1 20 Now I'm gonna pair that with the last cohesion. And since the last equation has just a plain X, I'm gonna go ahead and multiply by 10 as I'm writing it down. So Big 10 X plus 10 wa plus tensy equals 60. So I took this one times 10. So then, when I subtract these to get 10 watt close, 30 z equals 60. All right, I'm gonna repeat that process with the second and the third. So the second equation is 100 X plus 1 81 waas 3 20 easy and and a equals 1000 1060 hands. Not work. 1060 of it. The second equation noticed. Does it match up? So now let's multiply by 100 before we rewrite it. And so we get 100 eggs plus 100 y plus 100 z equals 600. So then when we subtract, we're gonna get 80. Why? Plus 220 easy equals for 60. Now we've reduced the system down to where we have a system of two burials and two equations. So we're gonna put those together. You notice your wives don't match. You have 80 and 10. So when you're writing those down paired him a, um, go ahead and multiplies. There were 80 close to 20 Z equals 4 60 And now, before I write this one, let's multiply by eight to make it 80. Why plus 240 z equals 480. Now when you subtract to get negative, 20 z equals negative 20 and C equals one. So I've got my see value. I can use my Z value. Remember the X equal to Z So that means in that X equals times one or two. So I've got ecstasy I need Why easiest want to do is the lax one. They're experts wife Rosie, Right after total to six. So explains why Plus Z has to equal six If you've already got +21 that means why has to be three in order for it to equal six. And so there are your three values for X y Z in this problem.

Let's up stock cuts. So it says and exercises 27 29. We see the number of advertised brand names, people recalled immediately after watching TV shows and 40 and 24 hours later. Strangely enough, it appears that they remembered more about the ads the next day. Should we conclude this is true in general about people's memory of TV ads? And then we're have four parts to the question part A says Suppose one analyst conducts a two sample hypothesis test to see if memory of brands advertised during violent TV shows is higher 24 hours later. If his P value is 0.13 what might he conclude? So that's a really small P value, and it doesn't tell us what Alfa level he used. But if he is using the generic 0.5 then we definitely have a significant results. So he would be able to reject his null hypothesis that his two groups have the same mean difference. So he's able to reject his no hypothesis because that is a significant result. So, Part B says, explain why his procedure was inappropriate. Which of the assumptions for imprints was violated. Okay, so this study asked the same people right after they watched the odds and 24 hours later. So because they're the same people in each group that they are comparing the results for, um are independence violation waas. Our independence assumption was violated. So independence and independence was violated because our researcher would ask to the same people before and 24 hours later, Um, their brand recall. And that is a matched pair design. And that is dependent. So the second sample is dependent on the first sample, so that does not hold independence. So Part C says how my the design of this experiment have tainted the results. Um so just like I discussed a little bit before the researcher used a matched pair design and a matched pair. Design is dependent. So his results are unreliable and his results were unreliable because our independence assumption was violated. So we have one more part. That's part C. And it says I'm sorry as part d suggested design that could compare immediate brand name recall with recall one day later so asking us to design our own experiment basically so I would have 60 subjects and they would all watch the program. And then I'm gonna have to groups and we are going to randomly assign an equals 32 each. And one group will be asked right away. So they're going to be asked about their brand recall right away. And the second group will be asked 24 hours later, and then we compare those results. So we're gonna compare brand recall and because there are different people in each of the groups and they were randomly assigned, we maintain our independence and we are able to have stronger statistical results at the end that are accurate and precise for us to use. Alright, guys, that's the end of this video. I hope you learned a lot, and I'll see you next time.


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