question a-f

Name: question a f
Uploaded: 2021-12-09
Duration: 2 min 17 s
Channel: Numerade
Description: question a-f

Question

question a-f

Marc Lauzon · Accepted Answer

is it equally likely that people choose rock, paper or scissors when playing the game. So you are correct in our hypotheses, the null hypothesis is the distribution is going to be uniform. It&#x27;s going to be the same across all categories. And then the alternative hypothesis is the distribution is not uniform, it&#x27;s not going to be the same across all categories. So to decide which one of these is true, we have to get a test statistic which is our chi square. Now for the Chi Square, I need an expected value. So we had 99 people here that That chose each one of these categories in total. And if it&#x27;s equally likely to choose each category, the expected counts are going to be 99 divided by three. So we would expect 33 people to choose rock, 33 people to choose paper, 33 people to choose scissors. And then to calculate our chi square, we do the observed value minus the expected value squared Divided by the expected count. And we do that for each category. So for paper it&#x27;s going to be 21 -33 Squared over 33 plus. And then Scissors, -33 squared Divided by 33. And when you calculate that out, we get a chi square value of 7.51. So that&#x27;s our test statistic. Now for the p value. Either using the chi square distribution critical value table or using technology. The p value for this comes out to be between 0.1 And .05. Now this p value is a pretty small P value, so that&#x27;s going to cause us to reject the null hypothesis. So we&#x27;re going to reject the null hypothesis. And you are right. In terms of the conclusion on this, the data provides sufficient evidence to claim that rock papers and scissors are not chosen equally as often as one another.

David Nguyen · Answer

Hi I&#x27;m David and I&#x27;m here to have you answered your question. Now let me bring up your question here into question here we will have the genders on the three Children. Um A certain family. As soon to be revealed out comes up. The cheaper it can be under the. Good point point point girl. Good point. Good point girl. Bye bye bye bye. Goodbye and goodbye. Fine. And the X ray will be defined first. Are it will be the number of the people and that if it is equal to the square Monastir, Monastir. And where have you been doing? Table here? The volume, the X. And the outcome. So when you need to convict the table from the barley on the X. And the proper put it in the X. We see that actually have only the very on the money to two and 10. So let&#x27;s try to stand from the smallest one will be managed to first And then two and then the 10 here. Actually could you manage to we see that it occurs and the value of This one will be managed to managed to managed to managed to. So we have the 1234 out of the 12345678. So we will have the four out of eight. Ah it would you go during the one out of two and from the X. F. 22 we see that only this one this one and this one So they go out here will be the three at age and for the last one we have for X equals 15. Only one outcomes there, they found the probability will be one out of eight and that&#x27;s gonna be the answer to this question here. So let me summarize it here for you. We have to act. And the probability of the X. X can have a very modest too. And it can probability for execute you will be the one half probably for exited CUBA. B three at eight for the actor to tend to be one of the eight.

Paul A. · Answer

Once again, welcome to a new problem. Uh This time we&#x27;re dealing with inferential statistics. And when it comes to uh inferential statistics, we have uh two branches we have categorical categorical variables. And we also have uh numerical variables. And when it comes to numerical variables we have um regression analysis as one of the options where we&#x27;re using the independent variable, the independent variable which is sometimes called the uh explanatory variable. And we designate this as X. And then we are also using the dependent variable which is also called the response variable. And we designate this as as why. Uh huh. The regression model involves a scatter plot for quantitative variables. This could be aged for example and this could be income. And so once you have the uh scatter plot you introduce a line of best fit. Why? Had equals two A plus B. X. Which seeks to estimate these points. The gap, the gap between a single point. Why, for example if this point is X comma y. So the gap between the point um why and the predicted value. That gap is called the residual. The residual error. The residual error. And so we have options, we can use we can use uh this line is called the least squares Line of best fit. Line of best fit. And it simplifies a relationship where we have some squares total uh becoming the same as uh sum of squares uh residual plus the sum of squares of the era. So sum of squares total uh is the same as the sum of squares of residual. Uh Sorry the summer square. So the sum of the total total sum of squares. The total sum of squares becomes the same as the uh huh Regression sum of squares. Regression sum of squares combined with the the sum of squares due to the error or the error. Uh, sum of squares. So that&#x27;s the relationship that you use to get the line of best fit. It&#x27;s a line that estimates the the average deviation. So we have points on some points uh, points above the line above the nine balanced balanced by points below the light. And this is the sole purpose of the line of best fit. So now we have a new problem. And in this problem we of data. Mm hmm. And the data shows by variants by vary it relationship relationship between between the X and y variable. Remember the X is the independent and the Y is the dependent. Mm hmm. And so we have uh the data table, This is X. This is why. And we&#x27;re going to have the numbers. 22.3 24.3 26.3 27.8, 20 9.7. and the y is 29.5, 24.7. 25 .4 and 21.1. These are the x. uh and the y value. And then on this side we have y minus Y, bao. Remember Weibo is the average for why? The average for wife. we wanted to get that average would have to take uh The entire sum of this column divided by the sample size. The sample size. And you could see is 1234. We have five points. So whatever sum you get that&#x27;s going to be that. So we have that column squared. And this is the same as the total sum of squares. So total uh huh sum of squares, that&#x27;s the first column. And then the second column we do have the regression sum of squares, regression sum of squares. And the formula for that is why I had minus the average. That gives us the regression sum of squares. And then the final column is going to give us the error sum of squares. The aero sum of squares. And the error sum of squares is y minus y. Hot. So that&#x27;s that&#x27;s our error. Uh summer squares. So why minus y hat? And Uh these columns represent some. So if we do the numbers here, we have 11, 15, 56, we have 15 5236. We have 2.1316. We have 0.5776. We have 25 points 60 36. And then we&#x27;re going to have a some right there. So the sum of this column, It&#x27;s the same as 54.99-0. And then we&#x27;ll repeat the same thing on the next column, 1967 8 1. We also have 4.3098. We have 0.0807. We have 4.2189. We have 18.4556. And then the sound for this column is the same as 46.7431. Um And then the last corner will have 2012. Uh this is 3.4745. This is 1.3830 1.67 and 0.5837. And then the sun mhm becomes the same as only square that 8.31668. And so our graph for the five points if you graph it we have this is your estimation of these points that you&#x27;re seeing. Um mm So this is why this is X. And if you start at 22 You&#x27;re gonna end up getting these numbers right here. 28 30. And then we&#x27;re going to have uh 32, 22, 26 28 30 And 32 like that. So these are the numbers we&#x27;re dealing with in the regression equation, y heart is the same as 56.91 -1.18 x. So the question in part a But it was saying the variation in the sample. Why values? Yeah. Mhm. That is not explained by the mm estimated linear relationship between X and Y. Uh He&#x27;s given by the so the variation in the sample Y values. That not explained by the estimated linear relationship between the X and y. Uh is obviously going to be given by the the error mm hmm sum of squares. The air, Osama squares. Mhm. Which for this data, this data is the same as 8.3168. This is the arrows and squares. And then uh in fact be in 40b mm. The variation explained mm. Yeah, the variation the rather the proportion the proportion mm of the total variation. Mhm explained by the linear relationship between X and Y. So the proportion of the total variation explained by the linear relationship uh between between X and why? Mm hmm is going to be So the proportion of the total variation explained by the linear relationship between X and y mm. It&#x27;s going to be given by Is going to be given by 46 46 .7431. Yeah. Mm hmm. The line of best fit is connected to the data. And then we&#x27;re going to say, uh the best fitz minimizes, mm hmm minimizes the residual mhm era mhm And the residual error as you can see his the era of summer squares. So, the residual error is the same as the mm hmm. It&#x27;s the same as the error sum of squares. And and that era some squares. In this case minimizes the mm hmm minimizes the uh error. A rock summer squares. Which in this case, which for the data is eight points 3168 for the data is 8.3168. Uh The variation of the sun. So these are these are the numbers. So uh so we had the residual sum of squares uh where the regression some squares. Mm hmm. And we also had residual simple squares. So again, uh the regression sum of squares shows the variation. So the variation, the variation explained by the linear relationship. That&#x27;s the X and Y. That gives us the regression sum of squares. And then the variation in the sample Y value. That&#x27;s not explained by the estimated lee in your relationship is given by the error some squares. And the line of best fit is the connect the data. The best fit minimizes the residual error. And for this data it&#x27;s uh 8.316. Hope you enjoy the problem. Feel free to send any questions or comments and have a wonderful day.

Paul A. · Answer

Once again, welcome to a new problem. Uh This time we&#x27;re dealing with inferential statistics. And when it comes to uh inferential statistics, we have uh two branches we have categorical categorical variables. And we also have uh numerical variables. And when it comes to numerical variables we have um regression analysis as one of the options where we&#x27;re using the independent variable, the independent variable which is sometimes called the uh explanatory variable. And we designate this as X. And then we are also using the dependent variable which is also called the response variable. And we designate this as as why. Uh huh. The regression model involves a scatter plot for quantitative variables. This could be aged for example and this could be income. And so once you have the uh scatter plot you introduce a line of best fit. Why? Had equals two A plus B. X. Which seeks to estimate these points. The gap, the gap between a single point. Why, for example if this point is X comma y. So the gap between the point um why and the predicted value. That gap is called the residual. The residual error. The residual error. And so we have options. We can use we can use uh this line is called the least squares line of best fit. Line of best feet. And it simplifies a relationship where we have some squares total uh becoming the same as uh sum of squares uh residual plus the sum of squares of the era. So sum of squares total uh is the same as the sum of squares of residual. Uh Sorry the summer square. So the sum of the total total sum of squares. The total sum of squares becomes the same as the uh huh Regression sum of squares. Regression sum of squares combined with the the sum of squares due to the error or the error. Uh, sum of squares. So that&#x27;s the relationship that you use to get the line of best fit. It&#x27;s a line that estimates the the average deviation. So we have points on some points uh, points above the line above the nine balanced balanced by points below the light. And this is the sole purpose of the line of best fit. So now we have a new problem. And in this problem we of data. Mm hmm. And the data shows by variants by vary it relationship relationship between between the X and y variable. Remember the X is the independent and the Y is the dependent. Mm hmm. And so we have uh the data table, This is X. This is why. And we&#x27;re going to have the numbers. 22.3 24.3 26.3 27.8, 20 9.7. and the y is 29.5, 24.7. 25 .4 and 21.1. These are the x. uh and the y value. And then on this side we have y minus Y, bao. Remember Weibo is the average for why? The average for wife. We wanted to get that average would have to take uh The entire sum of this column divided by the sample size. The sample size. And you could see is 1234. We have five points. So whatever sum you get, that&#x27;s going to be that. So we have that column squared. And this is the same as the total sum of squares. So total uh huh sum of squares, That&#x27;s the first column. And then the second column we do have the regression sum of squares, regression sum of squares. And the formula for that is why I had minus the average. That gives us the regression sum of squares. And then the final column is going to give us the error sum of squares. The air of summer squares. And the error sum of squares is y minus y. Hot. So that&#x27;s that&#x27;s our error. Uh summer squares. So why minus y hat? And Uh these columns represent some. So if we do the numbers here, we have 11, we have 15 5236. We have 2.1316. We have 0.5776. We have 25 points 60 36. And then we&#x27;re going to have a some right there. So the sum of this column, It&#x27;s the same as 54.99-0. And then we&#x27;ll repeat the same thing on the next column, 1967 8 1. We also have 4.3098. We have 0.0807. We have 4.2 on 89. We have 18.4556. And then the sound for this column is the same as 46.7431. Um And then the last corner will have 2012. Uh this is 3.4745. This is 1.3830, and 0.5837. And then the sun mhm becomes the same as only square that 8.31668. And so our graph for the five points if you graph it we have this is your estimation of these points that you&#x27;re seeing. Um mm So this is why this is X. And if you start at 22 You&#x27;re gonna end up getting these numbers right here. 28 30. And then we&#x27;re going to have uh 32, 22, 26 28 30 And 32 like that. So these are the numbers we&#x27;re dealing with in the regression equation, y heart is the same as 56.91 -1.28 x. So the question in part a But it was saying the variation in the sample. Why values? Yeah. Mhm. That is not explained by the mm estimated linear relationship between X and Y. Uh He&#x27;s given by the so the variation in the sample Y values. That not explained by the estimated linear relationship between the X and y. Uh is obviously going to be given by the the error mm hmm sum of squares. The air, Osama squares. Mhm. Which for this data, this data is the same as 8.3168. This is the arrows and squares. And then uh in fact be in 40b mm. The variation explained mm. Yeah, the variation the rather the proportion the proportion mm of the total variation. Mhm explained by the linear relationship between X and Y. So the proportion of the total variation explained by the linear relationship uh between between X and why? Mm hmm is going to be So the proportion of the total variation explained by the linear relationship between X and y mm. It&#x27;s going to be given by Is going to be given by 46 46 .7431. Yeah. Mm hmm. The line of best fit is connected to the data. And then we&#x27;re going to say, uh the best fitz minimizes, mm hmm minimizes the residual mhm era mhm And the residual error as you can see his the era of summer squares. So, the residual error is the same as the mm hmm. It&#x27;s the same as the error sum of squares. And and that era some squares. In this case minimizes the mm hmm minimizes the uh error. A rock summer squares. Which in this case, which for the data is eight points 3168 for the data is 8.3168. Uh The variation of the sun. So these are these are the numbers. So uh so we had the residual sum of squares uh where the regression some squares. Mm hmm. And we also had residual simple squares. So again, uh the regression sum of squares shows the variation. So the variation, the variation explained by the linear relationship. That&#x27;s the X and Y. That gives us the regression sum of squares. And then the variation in the sample Y value. That&#x27;s not explained by the estimated lee in your relationship is given by the era some squares. And the line of best fit is the connect the data. The best fit minimizes the residual error. And for this data it&#x27;s uh 8.316. Hope you enjoy the problem. Feel free to send any questions or comments and have a wonderful day

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