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The Professional Golfers Association (PGA) maintains data On performance and carnings for members of the PGA Tour: For the 2012 season Bubba Watson led all players ...

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The Professional Golfers Association (PGA) maintains data On performance and carnings for members of the PGA Tour: For the 2012 season Bubba Watson led all players in tOtal driving distance_ with an average of 309.2 yurds per drive. Some of the factors thought t0 influence driving distance ue club head speed, ball speed, and launch angle. For the 2012 season Bubba Watson had an average club head speed of 124.69 miles per hour: an average ball spced = of 184.98 miles per hour; and an average laun

The Professional Golfers Association (PGA) maintains data On performance and carnings for members of the PGA Tour: For the 2012 season Bubba Watson led all players in tOtal driving distance_ with an average of 309.2 yurds per drive. Some of the factors thought t0 influence driving distance ue club head speed, ball speed, and launch angle. For the 2012 season Bubba Watson had an average club head speed of 124.69 miles per hour: an average ball spced = of 184.98 miles per hour; and an average launch angle of 8.79 degrees. The WEBfile named PGADrivingDist contains data on total driving distance and the fac tors related driving distance for 190 members of the PGA Tour (PGA Tour website: November 2012). Descriptions for the variables in the data set follow Club Head Speed: Speed at which the club impacts the ball (mph) Ball Speed: Peak speed = of the golf ball at launch (mph) Launch Angle: Vertical launch angle of the ball immediately after leaving the club (degrees) Total Distance: The average number of yards per drive file DrivingDist



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Golf Robots. Serious golfers and golf equipment companies sometimes use golf equipment testing labs to obtain precise information about particular club heads, club shafts, and golf balls. One golfer requested information about the Jazz Fat Cat 5 -iron from Golf Laboratories, Inc. The company tested the club by using a robot to hit a Titleist NXT Tour ball six times with a head velocity of 85 miles per hour. The golfer wanted a club that, on average, would hit the ball more than 180 yards at that club speed. The total yards each ball traveled was as follows. $$\begin{array}{cccccc}\hline 180 & 187 & 181 & 182 & 185 & 181 \\\hline\end{array}$$ a. At the $5 \%$ significance level, do the data provide sufficient evidence to conclude that the club does what the golfer wants? (Note: The sample mean and sample standard deviation of the data are 182.7 yards and 2.7 yards, respectively.) b. Repeat part (a) for a test at the $1 \%$ significance level.

A hist a gram provides sample data with sample mean exper equals 291.9 Sample standard deviation S equals 8.343 And sample size N equals 186. This data is for the 186 best golfers mean drive. Using this info, we want to answer the following three questions. First part a let's construct a 95 interval for the population. Mean mute for the drive. So remember that the confidence interval is given by the formula X. Bar minus margin of error. E. Is less than you as an expert. Plus E. So we already have our X. Bar. We need to find the margin of error. E. So going over to the right of this dash line, we're going to solve for E and then plug back into the equation the left. Before we can find you have to identify the critical value for a. T. Distribution with degree of freedom and minus one equals 185. We specifically do so as a confidence level alpha equals 0.5 per the instructions to construct a 95% confidence interval. So human, the T distribution with this degree of freedom and this confidence level we can use a tea table to identify T equals 1.927 We convert this T. Value to a margin of error. E. Following the formula equals T. Times as a route and plugging the T. We just found With our sample data gives e equals 1.188. Now we can plug in our sample mean to 91 no margin of era 1.188 to obtain Confidence interval to 89.88 is less than you as less than 292.30. Now in part B want to answer, are there problems interpreting this interval? Yes. there are clear problems because this is not a random sample. The data is for the best golfers, not a random sample of golfers. Therefore we don't really want to interpret this interval. Finally, part C, the data points of themselves. Mean, as I mentioned, the other mean, drives for each golfer. Is this an issue? This is also an issue because it means that themselves less variable than individual drives, so this overall distribution or data set is less variable than it should be when represented by individual drives.

What's up dot cats? This is problem, 43 says Doesn't matter What kind of t a golfer places the ball on the company. That manufacturer, Stinger Tease, claims that the thinner shaft and smaller head will lessen drag, reduce spin and allow the ball to travel further. Hmm, a summary statistics from the test are shown right here. That's what they gave us. Assume that six balls were hit off of each T and that the data were suitable for inference. And then here we go. Is there evidence that balls hit off the Stinger teas would have a higher initial velocity. So we're testing ball velocity, and we want to know if Stinger teas have, ah, higher velocity than regular. So it would be our difference between our stinger minus our regular be equal to zero and then our alternative hypothesis. So that would be that are mean. Differences between Stinger and regular teas are greater than zero as we're predicting that Stinger has higher velocity. So let's go ahead to our calculator and put these numbers in and see what we actually have. So let's go over to the tests. We're going to hit 42 sample t test. We're gonna put ah, Stinger t information in first for ball velocity. So 1 28 83 is the mean 830.41 standard deviation. We were told that each sample sizes six and now we're going to do the regular T. And we want to know if Stinger has higher velocity pulled is going to be no calculate right away. We can look at RPI value and see that it's lower than 0.5 So we do have a significant results. Okay, so let's go ahead back to our white board. So our p value waas less than 0.5 So that means we can reject are null hypothesis. Oh, I am not. I don't know what I'm doing. All right. So we can reject are null hypothesis. And we can support our alternative. So evidence suggests that balls hit Stinger teas have higher the lost city and the regular good enough. Alright, guys, that's it for this video. I hope you learned a lot and I'll see you next time

Everyone today resolving problem number 20 Chapter two. Now, this is a four part problem. Impart a viewer asked to people with preconceived percent pregnancy in part B were asked to use our data frequency frequencies be populated part A to history. What's you were asked to describe? Their solution showed in this challenge and party. Um, again, we're asked for more descriptors is the, um if you notice anything abnormal about the destruction that also where the most frequently, Uh all right, So let's get started part in order to find the heart treatments easier going to look at the date given and from the data given, you can see that the frequency for 04999 is going to be 30. Then you're counting up from individual income existed. And, you know, by the way, before you had, you know, this is a sample size of 50 and then percent we didn't see, you know that you walked out the total 100% There is your children home. What? What's it? Where so then from 14,900? No, I it avoids second team one for tongue bad. 14,000 line between 50,000. 19,000. Why? Between 20,024 to between 25 1 line zero to this key 30,039 one value Which 40,000 four. Well, then between 45 49. Yeah, finally forceful wide. So they stopped? No, actually not actually based off their golf playing. But outside evolved so off course money to make there's wanted 1000 art Sanofi for some frequencies. What you're going to do is you're going to take each individual. You can see that you found well, underline the individual ones and then what you're gonna do is divided by the total 50 and multiply whatever decimal number. So just total 50 that beats before is that sample size. And then whatever you got us more is that individual present city divided by the total won't buy that by 100%. So how that looks in actuality is 30 divided by 50 is going to be 0.6. So that was what, six times 100 which is going to be 60% when you have nine fighter by 50 which is 500.1, and that results in basically hope you guys are nursing the pattern that it's just multiplying the frequency by two. So four times two is eight. It's your time to office. Just here to involve zero home. It's you survivors here. If you can see that I have talked with you percent frequency as well. Uh, where zero there. Um, now, moving forward. I have three here. So three times two is going to be 66%. And the reason I must find my tears because to see howto 50 for total immunity to get 2% you told. That's why I'd like to hear between $25,000.29,999 dollars. 4% frequency one times two, 3 40 44 And finally, 50,000. Love I have. That's how you fill out your freaking team for sex. All right. Moving on to heartbeat. You're asked to now construct a history on based off of the frequencies we've just found. Hey, So in order to do this, you should know that in a history, Graham, um, the heights is going to be representative. The frequency and then the width should be the same for each bar in your history. So what that's gonna look like is between bike A and 99999 So, actually, between zero and five K, we have 30. You do that? You gonna You're just gonna shave that in? You can much easier to do with the pond Bieber or pencil paper. Oh, I'm gonna write if you can see a 30 up above my, um then between five. And 999995999 I would have C nine. Just just for a little time. Yeah, and that's something like that. How did you do that? Sorry about that, guys. That's good. She got in right nine. It's kind of close to 10. Hopefully, guys can see that. That is No. But even if you can't see, this is the reason we write our numbers about the bars. Foreign person, grading their work. They know that. You know that. You can see is nice, Then between 10 k and 15 essentially 15 k, you got four between 15 and 20 year. You have zero. So you just don't shake anything in there. And you have 32 one in 25 day to between 5 30 Okay, she goes to again, just to reiterate a minute, right? You can see it bought the bar itself, just so nothing's up to chance. Then, between 30 and 39 999 Everything's playing. Um, but then I have you won 40 and 45 days. Nothing between 45 50. Carrie. And then anything about Dick Perry? I have, ah, frequency of one. So now that I have my history, Graham, what I can do is, um, that the sister gun. I can, um, pretty simply see what the shape of my distribution is going to look like, because clearly the majority of my numbers are going to be to be left side of Mr Graham. And when you have the majority of your data points to the left side, the way you describe the shape of your distribution is huge for sure. Now it's the opposite direction because I have the majority of my data points in the last side. So this would mean that distribution, the shape of this distribution on the history Graham is skewed, do you that you guys guess it to the right again. That's because it's the opposite direction. So pretty simple. There again. That's all based off of the graph that I just read. The history of my district seems mean, um, for the points to Geeta. All right, now in part, do you? I am going Thio Excuse me now in part D. I'm going Thio Figure out where the most frequent income is so most free goods most great. And remember, it's not actually 5000. It's actually 5,000,000 because it's times 1000. So within the right under 5,000,000 and begun our units just include the unit's whenever you can. Writing it doesn't hurt. And it could actually help in the description, especially in statistics. They got 5,000,000 may be right that sorry about that. I and then I'm gonna at six year olds. And then the last question kind of a tag along question. Do this main question asked in party about the most reprints income last. So we're asked to kind of describe anything else that's six out on dhe based off of the individual golfers. And I would say that Tiger Woods and Phil Mickelson, it's high here, especially tiger again. What I'm doing right now is I'm looking at out liars in my history so clearly, Bill, right there and tiger, right? They're gonna represent two out lives. That's why I am putting it in my description in party because it's just another opportunity to describe something important about the distribution. So Tiger and Phil make a lot speak musically in the lock and cops, and I'm gonna draw narrow, essentially saying that they are out liars in my data set. I know for sure that tigers I'm pretty sure that Phyllis there is a mathematical way to figure it out. Um, it's basically the upper route. The 23 values 75th percentile added times 1.5 times interport tire range. And if that is, if the value for from Mickelson in spirited in that database it out because that's our upper bound. But I think for sure that these two are out fires just because we do have 30 from 0 to 5,000,000. So they are. And if you know anything about golf, you know that's higher with Phil Mickelson. Urge to mate famous most famous male family most famous male golfers of all time. Um, well, at least in the 21st century, so shots on my golf fans and I hope you all enjoyed my explanation

For the given problem, we're talking about the record golf stroke. The fastest golf ball speed ever recorded is 91.1 m/s, which is 204 mph. So we're gonna be looking at the horizontal range which is R equals be not to be not squared. Yeah, over a G I am sign theater cooking peter book called Synnex code Synnex and we know that the initial velocity um we know that the most, the ideal angle would be 45 degrees. That's because if we pick any value, what should say the initial velocity is Is 100 or 10 for example. Um Then what we end up getting is that since this is a function of X, We can consider the fact that G is equal to 9.8. Um And this right here is going to give us the result. We see the maximum range is going to be when our fate of value is equal to 45°, which is right here. So that is the final result we achieve


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