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The head of Marketing at American Expresso interested in determining whether the average income of its credit card holders has increased over the past 14 years. Whe...

Question

The head of Marketing at American Expresso interested in determining whether the average income of its credit card holders has increased over the past 14 years. When the credit cards were first marketed_ the mean income of all card holders was equal s60,000 per annum_ The results of the corresponding hypothesis test that was carried out are shown here_AMERICANahm teeEXPRESSO INCOME TESTAccording to the hypothesis test results_ is most reasonable to conclude that:approximately 99.09% of American

The head of Marketing at American Expresso interested in determining whether the average income of its credit card holders has increased over the past 14 years. When the credit cards were first marketed_ the mean income of all card holders was equal s60,000 per annum_ The results of the corresponding hypothesis test that was carried out are shown here_ AMERICAN ahm tee EXPRESSO INCOME TEST According to the hypothesis test results_ is most reasonable to conclude that: approximately 99.09% of American Expresso credit card holders have an income greater than 560,000 per annum there is evidence supporting the hypothesis that the mean income of American Expresso credit card holders is now greater than $60,000 per annum there is 99.090 chance that the mean income of American Expresso credit card holders is now greater than 560,000 per annum the mean income of American Expresso credit card holders is now greater than $60,000 per annum Ho: p Ha: / s60,000 per annum 560,000 per annum 0.05 562,463 per annum 57,000 per annum 2.36 0.0091 P-value Outcome: REJECT THE NULL



Answers

Use the technology of your choice to conduct the required chi-square goodness-of-fit test. Credit Card Marketing. According to market research by Brittain Associates, published in an issue of American Demographics, the income distribution of adult Internet users closely mirrors that of credit card applicants. That is exactly what many major credit card issuers want to hear because they hope to replace direct mail marketing with more deficient Web-based marketing. Following is an income distribution for credit card applicants. $$\begin{array}{l|c} \hline \text { Income (\$1000) } & \text { Percentage } \\ \hline \text { Under } 30 & 28 \\ \text { 30-under 50 } & 33 \\ \text { 50-under 70 } & 21 \\ \text { 70 or more } & 18 \\ \hline \end{array}$$ A random sample of 109 adult Internet users yielded the following income distribution. $$\begin{array}{l|c} \hline \text { Income (\$1000) } & \text { Frequency } \\ \hline \text { Under 30 } & 25 \\ \text { 30-under 50 } & 29 \\ \text { 50-under 70 } & 26 \\ \text { 70 or more } & 29 \\ \hline \end{array}$$ a. Decide, at the $5 \%$ significance level, whether the data do not support the claim by Brittain Associates. b. Repeat part (a) at the $10 \%$ significance level.

So this question is quite a long question. Looking at income and housing, which is originally from chapter six, Extras 32 I've written on the left all the important days that we're gonna need as one of the rough sketch. So let's start with pot. A part A is asking us is restrict those of regression analysis appropriate. Now, for this is just a simple as looking our plot and what we're looking for is some kind of linear trend. Now, if I was drove around something like that or even a little bit learn something like that, you can see that that is a positive relationship on something that you can see could show linear trend. So I would definitely say, based on that graph, you need to say yes. So, Pop be is asking us what the equation is that predicts the housing cost index from the medium family income. This is where we're gonna need this data on the corrosion above it as well. So the main equations you're gonna need to marry for this is that be, is all correlation times a stunt deviation of why over Austin, a deviation off x a is I mean why? Which is often written as why about hair used mu A minus bi axle not be is to be from the first Parisian. So we need to look out. Be first and these were work. Now, if we have ah, regression equation that looks like something like this. This is what the a and the B what we're trying to work out now. As we are predicting housing cost index housing cost index is all why? Which leaves meeting from the income as our X. So now I just need to subtitle the right values. And do you have a baby? Is that all of the correlation, which is no 0.6 life? Well, times are by standard deviation of why which is our hatred, Alex 116.55 And that is over the standing ovation of X, which is seven. A 72.4 to. That's in your answer. No point. Not 17 now a. We need to take a mean of why which is 338.2. Only kneed Teoh minus be times all mean of X. I mean, if x is 4 6200 32 that you fool, sir. And that gives us an answer to a of minor since point from the sign minus under gruesome 0.6 full. So we put all that together to give Haixia. But little, however, um is 557.6 full class No find not well, 17 And then our X is, um I the is a Christian we're gonna be using in the rest of this question Looking put C Part C is asking us with a state with an M if I of 44,193 what would our predicted Hate CRB And this is just a simple substitution case. So we're gonna do well. Haiti. I is Mona's 157.6 full Plus no point no. +17 And then I am If I we are told it's 44. None. No, sorry. And that's what we need to do. We just need to something it gives us now. NSA 323 point 79 rounded to two. There's more places. That's the answer part. C d is gonna use our answer from parts. See, because it's asking us if Washington D. C has an Emam 5 44,993 Onda Hate See, I have 548.0 to how far off is our prediction in parts See on this is effectively asking us for the residual. So for this one, we need to dio 148. What 02 is is what we are told is the actual value I mean to take away from the all prediction No, which gives us an answer 224.2 three. So what was that saying is our prediction was 224.23 lower than the actual value on the last two passes Question But looking at standardizing variable So party asked if we standardize both are variables What would be the regression equation that predicts the standard Haiti I from the standard MF I on when you standardize variable It's been represented by Zet. So for this one, we would be are standardized. Hey, see Copy Onda. We want to know how we gonna predict that. It's quite simple, really. We just need to use on a correlation. We just times standardized I'm a fly by that correlation, that's for you need to do similarly part effort else's to do it the other way around. So now we're predicting em. If I from Haiti on with coronation, it works both by around, so we need to do exactly the same thing age. So it's just the opposite of party.

This is a problem. # 29 We are given a set of data regarding regarding the per capita disposable income for each of the 50 States and District Columbia. First we will construct a frequency distribution Given that the lower bound of our class is 20,000 and our class with our 2500. We will get the following for our income. Mhm. I'll just round both of these classes to make it easier to fit. So we have 20- 25 K. 22.5. Mhm. 22 5-25, 25-27 5 27.5-30 30 to 32.5 32 5-35, 35 to 37.5 37 5 to 40 and finally 40- 42.5. Now these are not inclusive of the bounds. This is obviously this will be like 22499, I just ordered like this to make it easier to ride out for our frequencies. If we count each of these data points, we get the following three, 10, 14, 12, seven, two, two, zero and one. And when we calculate our relative frequency we get 5.9%,, 19.6%,, 27.5%,, 23.5%,, 13.7%,, 3.9%,, 3.9%,, 0% And 2.0%. So as we can see most of our data is in the top part of our data set. And when you construct your hissed a gram, it does seem to follow this so it is very slightly right skewed. If we are then to change our class sizes to be 4000 wide you will find that the data is significantly more skewed left as our relative frequencies will drop to 19.6%,, 43 0.1% 27.5%,, 5.9 And 2% for the last two classes that we would have. So as you can see, this data is significantly more right. Skewed. This set of data with these smaller classes is a much more precise way of representing this data.


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