the-following-data-show-the-number-of-rental-cars-in-service-for-three-rental-car-companies-hert-avi

Question

The following data show the number of rental cars in service for three rental car companies:
Hert. Avis, and Dollar. The data are for the years $2007-2010$ and are in thousands of
vehicles (Auto Rental News website, May $15,2011 )$ .
a. Construct a time series graph for the years 2007 to 2010 showing the number of rental
cars in service for each company. Show the time series for all three companies on the
same graph.
b. Comment on who appears to be the market share leader and how the market shares are
changing over time.
c. Construct a bar chart showing rental cars in service for $2010 .$ Is this chart based on
cross-sectional or time series data?

Mihir Nayar · Accepted Answer

Hey, everyone, today we&#x27;re solving problem number 14. Uh um chocolate in section two of your textbook. So let&#x27;s jump right into it. In part A. You&#x27;re asked to draw time series graph, um, off the car sales for all three companies from 2007 to 2000 Tech. So, um, in times, years graphs, When you&#x27;re making them the year or any, you know, the time element always goes on the Y axes and then your number of cars and service I&#x27;ll just write cars here will always go about their variable Essentially will always go on the x axis. I mean, on the y axes, whereas the time always goes on the X axis is so again we have 07 08 So I and just 10 something like that. 07 I got 07 is representative of the year 2007 08 is representative of the year 2008 09 is representative of the year 2000 and nine and finally, 10 was the representative of the year 2010. All right, And then you look at your maximum value in terms of number of cars and service and top and thousands. And for hurts, it&#x27;s somewhere above 300 but below 350. So I&#x27;m gonna make a scale by 50 for this particular problem, Hogan. 350. I wasn&#x27;t course. And service is going to be my max for my wife. Value on the scale at least. Not like Max about you. I&#x27;m gonna go by fifties of 50. 100 1 50 200. I want too small. Go. 50 100. 150. 200. 250. 300. So I can just leave it by 50. So you have 50 and obviously this would be 100 101 150 would be here then. I don&#x27;t know the 5200. And then you have 250 here so again goes up by fifties. All right, now we&#x27;re time. It&#x27;s time to grab. Um, I recommend making key here. So right. A key for your graph, in part at least. And the reason for making he is to kind of just show what different colors if you&#x27;re using different colors when you&#x27;re drawing this final answer or different shapes. So like if I had a star on with different instead of a dot on them in like an ex The ex represent Avis story represent hurts don&#x27;t represent dollar. You could do something like that. But since I have the colors on this my port, I&#x27;m going to utilize that. So, God, for my key for a I&#x27;m going to say anything red. So ride thought or a red line is always gonna, um, indicate something about their hurts. Car company. All right, then we&#x27;ll say green. It&#x27;s a green dot or green line would be indicative of values for Avis and the line that we&#x27;re gonna make it. And then last but not least, I have blue. So blue obviously has to represent anything blue on my graph pasta represent information regarding dollars company for their cars and servers from 2007 to 2010. So now we&#x27;re just basically in a graft. The data, um for hurts. I can see that I&#x27;m going to have a raffle. It&#x27;s like this. So a little bit about 2 300 then a little bit below that. But still look 300 that dips below. I&#x27;m drinking too, that it picks back up just a little bit in 2000 gone straight lines. Probably easier. D&#x27;oh! With a pen and paper on. Then we&#x27;re moving on to Avis again. This is just graphing Tina points, guys. So in 2007 Avis, how little bit over 200,000 Parcel service that I went off in 2008 beholding about 2 52,009 It&#x27;s shot up close to 300 and then, oh, Tana, dip below Hertz value. But again, just by a little bit. Not too much. So again, connect the dots with straight lines, try a bus to make it street and the beautiful thing about her keys. Now we don&#x27;t have to tell her. We already told our reader with our key, but all the colors, record sights. Um, So with dollar above 1 50 it started out in 07 That in 08 Um, it dipped below 1 50 Just minimally, I think, 09 dipped a lot 10 just but very even space. Not much difference in 09 and 10 for a dollar. So there you have it. There&#x27;s your times. Here&#x27;s Graf again with times, Here&#x27;s graphs you connect all your points of straight lines and on the X axis is always going to be your time. All of it. Moving on to part two. Any of the questions which asks us for the first part Time to figure out what the market share linger is in terms of, um, number of car sell sold in thousands from 2070 laws and attend. So if I look at my graph, I see specifically that the red is leading the charge and the red is hurts, So hurts gonna be you&#x27;re a guy. This is all based off of the graph you just drew, as will typically be the questions with stats, they&#x27;ll follow previous part Always. So that&#x27;s something good about it. All right? Hertz is your leader. And then if you just wanted to notice different graphical trends, which they do ask about, um, I&#x27;ll just say it out loud for you guys. So Hertz had a general decrease in sales overall, um, they picked up a little bit from 09 to 10 but overall decrease, um A. This was the one that had a drastic increase, especially from 2008 to 2009. But then they had a bit of a dip so leveled off in 2010. But it&#x27;s still increased overall from 07 to 10. And then finally, dollar howto probably. Yeah, it did have the biggest decrease in cars in service. Uh, there you have it. That&#x27;s kind of the brief summer you give and then in part, see your astronaut. You are asked to now draw another grab this time a park, Um, for rental cars in service in 2006. I&#x27;m just gonna draw by two axes. Mom, again, The year 2000 and 10 is going to be on your ex axes. The different bars are gonna be representative of different companies. So I would have again, I&#x27;m using this key for both grafts. So this would apply to this and then this he would have lied about. So I&#x27;m just going to make a red mark for Hertz. I got nuts. The beauty of your key could apply to more than one draft if you are soft and more than one part and need to draw a graph into the parts of the question So we know that route is representative. Anything regarding hurts information. Green is representative of anything regarding a this information. And finally, Blue&#x27;s representative of anything. Great party dollars affirmation and the number, parts and service. And again, um, you&#x27;re why axes is going to be the same again. It&#x27;s the number of cars and service I&#x27;m not writing. Got out fully. So just like ours. You guys were aware of that. And now we are going to draw our Marga. Um, but the first thing you&#x27;d use to make a scale for a buy axes I would choose to start it. Zero kind of drops with lying to show. Get somewhere else that&#x27;s larger. This is 100 right here. Um, and from 100 onwards in our y axes, I would go up by 25 1 25 1 50 We need to get to 300. Rubber that to 25 2 50 She was 75 300 25. So I&#x27;m gonna make that bigger. It&#x27;s home of space that I just like a 1 25 12 one said to home drug 25 Do you for certainly 3 25 there. So I&#x27;m just gonna mark I&#x27;m Jake. I mean, the fifties. So 350 200 that all right, now we&#x27;re going to draw our three our army, our three traps. Where? Each individual. So again, you&#x27;re only asked about the year 2010. So for Hertz, in 2000 and 10 I had a value of 290,000. So get to 90 somewhere out there, Draw wine there to shave it in. Try your best to shit in. And I&#x27;m going to write the value on top of the bar two. All right, um, for Davis in 2000 and 10 my value. Well, I cz 270 so that&#x27;s gonna be kind of somewhere, but not exactly height, too. Not the same. Height. Never gets as by hurts, Bill, but it&#x27;s still pretty solid. 270,000 got shade that in much easier dependent papers. 270,000. And then finally, dollar, which did the worst, Uh, it had in 2010. Uh, a total of 100. 1000. We&#x27;ll be out here 18 Shape that in 108 And there you have it. That is how you saw problem number 14 from chapter one of the text. If you guys enjoyed my video, please of the light. But next to it I hope you all have a nice day. And thank you for watching.

Zach Steedman · Answer

all right. In a couple of my previous videos, I went ahead and calculated the means variances and standard deviations by hand. I&#x27;m not gonna do that because this textbook assumes that we kind of have Microsoft excel. And so I&#x27;m actually thinking being better use of our time to show you how you can broke plug this into Excel or Google sheets, which is what I use to find those three values. Okay, so the first thing we need to do is mean where you type in is your type in average, after you type in average. Oh, put equal shirts Excuse me, but equals a V. And once you do, a V average will probably pop up, select it and then highlight all the cells. So I am put it all this data into people sheets highlighted all the cells and it spit out the average. Oh, I guess I didn&#x27;t put that number similar to variants, right? Type of equal v a r. And you can see it&#x27;s the 1st 1 that comes up similar to standard deviation for standard deviation type in sd Dev. And then it should come up. And so here are the three values after and for all those you&#x27;re selecting the cells and clicking Enter. Right, Um so hear those three values That means 38 the variances 97 the standard deviation is 9.8 in variance and standard deviation are different ways to kind of say how much this data fluctuates and or how close it is to the mean. And so when we compare it to the West, the mean is exactly the same. So we can say, on average, you would pay the same amount of money per day on the West with these West Coast cities, as you would on these East Coast cities. However, the variants on the West Coast is a lot smaller, and so is the standard deviation, which is another way to measure how close we are to the mean. So if we had these numbers for the West Coast cities are imagined, they would all be a lot closer to 38. So you can see here this one gets all the way up to 58 all the way down to 30 I imagine for the West Coast cities, we&#x27;d be in the high thirties. Low forties, probably wouldn&#x27;t have any in the fifties or the twenties, we would all remain a lot closer to that mean compared to these East Coast cities where there are several different prices.

Julian Gerber · Answer

So we have the function in two variables. C equals 40 d plus 400.15 m, and what this function is representing is the cost C of renting a car for D days and traveling and Miles. Um So, for example, if we have the, um Value or the argument f of three comma 200 we could just input three and 200 as the values off D and M&#x27;s, this becomes 40 times three plus 0.15 times 200 40 times three is 1 20 plus 0.15 times 200 is just 30 which equals $150. So what this is saying is if you rent a car for three days and you drive 200 miles, then it will cost you $150 More generally, if we have the function f of three com a. M, we can do the same thing. We can substitute three and for D, and we just have 15.15 m. This is the same thing as 1 20 plus 0.15 m equals cost. If we see this equation, here is just a linear function in one variable where 120 is the why intercept 1200.15 is a slope. M is the independent variable and C is the dependent variable. So if we make a coordinate plain, um, where we have, um, the X and Y axes or the M and C axes, then we can grab this linear function. So we&#x27;ll call this, um m and the sea. So if m increases by 100 that&#x27;s our scale on the M axis and on the sea access, um, it increases by 25 hums. That&#x27;s 5100 1 50 So if we graph this, um, why intercept is 120? So that&#x27;s around, um, here and the slope this 0.15 which means that if you increase em, if you increase the number of miles by one, the cost will increase by 15 cents, or because our scale of the M axis is 100. If you increase in by 100 the cost increases by 15. So if this is 1 20 if m is 100 than that becomes 1 35 um, just a little bit higher and is 200 then that becomes 1 50 Um, if M is 300 than that becomes, um, 1 65 And you keep going until you have this linear function, which is just 1 20 plus 0.15 a M equals C. And what this is just representing is the cost of renting the car. Um, if you know that your only renting it for three days similarly, you can have a function of, um, de instead of em where m is 100. So in that case, you have 40 d plus 0.15 times 100 is just 15. So if we graph that function, um, then you have, um Then you have, um, a another linear equation Where in this case, um, the independent variable is days and the dependent variable is still cost. Um, so we know we can say that days are increasing by scale of one. And, um, will say this is increasing by 20 dollars. So we know the Y intercept is 15. Um, so that is around rate here. And for every, um, day, we add, because of slope is 40 for every one day, the cost increases by 40 dollars. So when d is equal toe one, we have 40 plus 15 was gonna be 55. So it&#x27;s around up here when d is too. We have 80 plus 15. Um, so we have to add another 40 to 55. That becomes 95. Um, around up there, when we have d equals three, we have to add another 40 to 95 that becomes 1 35 sets around up there and we get, um, a rough sketch of the line 40 D plus 15 equals C. And just like the last graph, this is just a linear equation where if we hold the miles constant as 100 miles and you increase the number of days by one on the cost increases by 40 because that is a slope.

Robin Corrigan · Answer

We&#x27;re given the following two independent and random samples of car rental rates from Boston and New York City and were asked to construct a 95% confidence interval on the difference in average rates between the two cities. So we&#x27;re asked for and 95% confidence interval for the difference in the mean rates. So we can say Mun is the mean for New York City, and you be is the mean for Boston. So our confidence interval is defined by the difference of the sample averages, plus or minus the critical value. Tens of square root of the New York sample variance invited by New York sample size plus the Boston sample variance over the size of the Boston sample. Okay. And from our table that I&#x27;ve presented here, we have everything except for the critical value. So to find the critical value, we need to know the degrees of freedom. Since we&#x27;re calculating this manually, we&#x27;re going to use the smaller of the sample sizes minus one. So they&#x27;re smaller. Sample is Boston, which is of size 10 so we can use end of Boston minus one, just nine, and then we can go to our table and look up the T value. So using nine degrees of freedom and we&#x27;re doing a 95% confidence interval, we get 2.262 And again, that&#x27;s taking this information and this information find this Valley and Snow. So now we can substitute all these numbers into our equation. And so for the Kaufmans interval. So we have 16 minus 10 plus or minus 2.262 and this comes out to you 2137 2 42 42 25. And you can retain the units if you like. So these they&#x27;re actually dollars. So we&#x27;re 95% confident that the true difference between the rental rates in Boston and New York City is between 2137 42 25.

Sid Wan · Answer

can number seventy four to cost to rent a small South Korea&#x27;s thirty line orders per day or fraction off a day is the car&#x27;s picked up beach cargo and dropped off in San Luis. There is a fixed twenty seven drop off charge. Let&#x27;s see. Axe represents the cost ofthe renting the car for X days. Thinking from Scotland, Slanderous finds a following. First, we just need to find the function ofthe sea yaks. Those axes like Haman days. You rent the car. See X is a cost in total. So it&#x27;s thirty nine dollars per day. So thirty ly ex Dave plus a drop off fee toe in this other guy that&#x27;s here and say We want to find sea off two over certain. So you just plug into a nursery. So thirty Certainly I do want us race certain, But Battle twenty six, Class twenty seven, which is fifty three and B. We want Foreign Sea off eight over, and I so still your plan in number. Certainly I might apply. You are a blind man, a twenty seven, which equals some fraction of anyone so warm. Eighty five over three and see. See, Juan, you&#x27;ve got to stop lagging one twenty three like last twenty seven, which is sixty six. Andy. We got one seal, one over one and three over football. It was just thirty line, but black three. Over. I guess it&#x27;s just seven over full. Plus twenty seven and thirty line. What did bless other? Yeah, two, seventy three or four plus his guys. Okay, so three eighty you ours. And he find the cost of rangers car for four point seven days. Who clocked in just four points. All right. Okay. Guys like I do thirty line, but five, four point seven equals glass. Twenty seven, two hundred and ten point three in next one. Graft, like was C X Focus. It&#x27;s so it was the intercept twenty seven. Look, you can&#x27;t You&#x27;re no beans from zero to infinity, I guess. And slow is twenty live. So fly twenty seven. You can put a one point one is Pacific&#x27;s and is here function. Yes, it is a function explain because every ex corresponds to one well value. You see a linear function? Yes, because clearly is just once reply. What is independent, Maribel? Independent horrible acts. What is a dip in the world? Boys? See extra cost defendant. Okay, Come

Ankit Gupta · Answer

so no. In this question, the question which we have to fall will be. Why is equal to 1 20 eggs plus 65. So So 1 20 is basically dollar 1 20 is for for day on 65 is additional for insurance. So now we will see the blood. So now, according to this plot, odd line will come from Tzeitel. This where the equation for this life is Why is equals to 1 20 x bless 65. No, it is asking what is if the why intercept in meaning So part ceases, it will be zero almost 65. There on the explanation is the base cost. Do the rent. Oh, the God is donor 65 and now another next part? No. For two days, the rent will be. Why is equals to 1 20 excess for days plus 65. So therefore, why is equals to dollar 305. Similarly we will find for five days. So for five days it will be. Why is equals to 1 20 into five multiplied with five plus 65. Therefore, why would be dollars 6 65 and for seven days Why is equals to 1 20 multiplied with seven plus 65. So therefore are why is equals to dollar 905. So now we will compare the we clear it. So if we can create with the equation which is why I use because toe 1 20 well replied with seven which is equals and plus 65 which is because too wise equals $2. 905. And it was given that weekly Do you is dollar 7 99 So therefore our weekly rate is less This is less so No, If there is a six person judge so what will be the total cost? So first we will calculate Why is it closed for four days? So why is it goes to 1 20 multiplied with four? It is because 65 plus 65 So why is equals to 5 45 And this will be a plus 6% charge on this So we have to calculate, define and value off Why so therefore why is equal to 5 45 plus 6% off 5 45 32.7 So therefore which is request toe dolar 5 77 0.70 No, uh, last but with cities. So the statement would be no in the car in every way can not being get Do so. Therefore X cannot be negative, so x can not will be. Thank you.

Problem

Every year, the U.S. Coast Guard collects data an…

Problem 14 Hard Difficulty

Answer

a. See graph
b. Hertz
c. Time series

Related Courses

Essentials of Modern Business Statistics

Related Topics

Discussion

Top Intro Stats / AP Statistics Educators

Srikar K.

Megan C.

Michael J.

Joseph L.

Intro Stats / AP Statistics Courses

Data And Variables

Data And Variables - Example 1

Recommended Videos

Watch More Solved Questions in Chapter 1

Video Transcript

David R. Anderson, Dennis J. Sweeney,Thomas A. Williams

Essentials of Modern Business Statistics

Srikar K.

Megan C.

Michael J.

Joseph L.

Data And Variables

Data And Variables - Example 1

What do you need help with?

Textbooks

Ask a question

Courses

AI Tutor

a. See graphb. Hertzc. Time series

Essentials of Modern Business Statistics

Srikar K.

Megan C.

Michael J.

Joseph L.

Data And Variables

Data And Variables - Example 1

David R. Anderson, Dennis J. Sweeney,Thomas A. WilliamsEssentials of Modern Business Statistics

Srikar K.

Megan C.

Michael J.

Joseph L.

a. See graph
b. Hertz
c. Time series

David R. Anderson, Dennis J. Sweeney,Thomas A. Williams

Essentials of Modern Business Statistics