Exaple in the given image.Answer the another image. Example: Coin FLIP• A coin can have a two probable outcomes, which are heads and tails.• We can say that when we flip a coin, there is a 50% chance for a headand 50% for tail as a result, thus, there will 50:50 or 1:1 ratio.• As an example, I flipped a coin 100 times. I got a result of 54 headsand 46 tails. We already know that there is 50:50 or 1:1 ratio aspossible outcome. We can say that the expected outcome should be50 heads and 50 tails.• So the Chi Square Statistic/Test, can answer the question:Does my result (54 heads and 46 tails) is equal to the expected ratio?Does my result (54 heads and 46 tails) deviated to the expected ratio?Let us define first which is Observed and Expected,then, simply substitute it in the formula given.E© -EY -50(54-50), (46-50)²E50You can also use tables like this:(43°(-4)Observed Expected10-E5050E1616Heads54500.32%3D+5050Tails46500.320.32 + 0.32%3DE 10-EF0.64= 0.64Student: Sir, Is that all?• Not Yet, We just computed the Chi Square (x³) value for that exampleCritical values for x test0.10.05 0.01 0.005• We should also know the dF or degrees of freedom*dF = n-1 ; where number of classes or categories1 2.706 3.846.64 7.8824.605 5.99 9.2110.603 6.251 7.82 11.35 12.944 7.779 9.49• We should compare it with theCritical Values of the x? Distribution (Table)13.28 14.865 9.236 11.07 15.09 16.756 10.65 12.59 16.81 18.557 12.02 14.07 18.48 20.2813.36 15.51 20.09 21.96• Commonly used significance level is 0.05 or 5%89 14.68 16.92 21.67 23.5910 15.99 18.31 23.21 25.19• From the example, there are only two outcomes (head or tail) so wesubstitute 2 for n, then we can compute for dFdF = n-1 ; dF = 2-1; dF = 1• From the table, the critical value for dF=1 at 0.05 significance level is3.84• The calculated x value is 0.64. Comparing it with 3.84, it is less than.0.64 < 3.84, so the null hypothesis (1:1 ratio/ O=E) is accepted.• We can now say that the result of flip coin with 54 Heads and 46 Tailsconform with the 1:1 ratio 1. Rolling of dice can have 6 different outcomes. A teacher rolled the dice 50 timesand attained these following results:710987a) Calculate the chi square value. Show your computation.b) Will the result of chi square follows the 1:1:1:1:1:1 ratio at 0.05 significance level?Why or why not?

Given that Rolling of dice have 6 different outcomes That are : 7 (ones) , 10( twos), 8(threes),…

1. Rolling of dice can have 6 different outcomes. A teacher rolled the dice 50 times and attained these following results: 7 10 9 8 7 a) Calculate the chi square value. Show your computation. b) Will the result of chi square follows the 1:1:1:1:1:1 ratio at 0.05 significance level? Why or why not?

1. Rolling of dice can have 6 different outcomes. A teacher rolled the dice 50 times and attained these following results: 7 10 9 8 7 a) Calculate the chi square value. Show your computation. b) Will the result of chi square follows the 1:1:1:1:1:1 ratio at 0.05 significance level? Why or why not?

Algebra and Trigonometry (MindTap Course List)

4th Edition

ISBN:9781305071742

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter14: Counting And Probability

Section14.FOM: Focus On Modeling: The Monte Carlo Method

Problem 3P: Dividing a JackpotA game between two players consists of tossing a coin. Player A gets a point if...

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Dividing a Jackpot A game between two pIayers consists of tossing coin. Player A gets a point if the coin shows heads, and player B gets a point if it shows tails. The first player to get six points wins an $8000 jackpot. As it happens, the police raid the place when player A has five points and B has three points. After everyone has calmed down, how should the jackpot be divided between the two players? In other words, what is the probability of A winning (and that of B winning) if the game were to continue? The French mathematicians Pascal and Fermat corresponded about this problem, and both came to the same correct conclusion (though by very different reasoning's). Their friend Roberval disagreed with both of them. He argued that player A has probability of Winning, because the game can end in the four ways H, TH, TTH, TTT, and in three of these, A wins. Roberval’s reasoning was wrong. Continue the game from the point at which it was interrupted, using either a coin or a modeling program. Perform this experiment 80 or more times, and estimate the probability that player A wins. Calculate the probability that player A wins. Compare with your estimate from part (a).
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Dividing a JackpotA game between two players consists of tossing a coin. Player A gets a point if the coin shows heads, and player B gets a point if it shows tails. The first player to get six points wins an 8,000 jackpot. As it happens, the police raid the place when player A has five points and B has three points. After everyone has calmed down, how should the jackpot be divided between the two players? In other words, what is the probability of A winning and that of B winning if the game were to continue? The French Mathematician Pascal and Fermat corresponded about this problem, and both came to the same correct calculations though by very different reasonings. Their friend Roberval disagreed with both of them. He argued that player A has probability 34 of winning, because the game can end in the four ways H, TH, TTH, TTT and in three of these, A wins. Robervals reasoning was wrong. a Continue the game from the point at which it was interrupted, using either a coin or a modeling program. Perform the experiment 80 or more times, and estimate the probability that player A wins. bCalculate the probability that player A wins. Compare with your estimate from part a.