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Answer all parts fuel additive is claimed t0 increase the power output of an internal combustion engine The performance of 10 engines are compared with and without ...

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Answer all parts fuel additive is claimed t0 increase the power output of an internal combustion engine The performance of 10 engines are compared with and without the fuel additive t0 verify the claims of the fuel additive manufacturer_ The results from these tests are shown in Table 5. (Question 5.xlsx)Question 5.xlsx Car Without Additive kW With Additive kWTable 5A. Power Output of 10 Cars With and Without Fuel additive.Using an Alpha value of 0.05 determine if there is evidence of an increas

Answer all parts fuel additive is claimed t0 increase the power output of an internal combustion engine The performance of 10 engines are compared with and without the fuel additive t0 verify the claims of the fuel additive manufacturer_ The results from these tests are shown in Table 5. (Question 5.xlsx) Question 5.xlsx Car Without Additive kW With Additive kW Table 5A. Power Output of 10 Cars With and Without Fuel additive. Using an Alpha value of 0.05 determine if there is evidence of an increase in the power output from the engines when using the fuel additive Indicate the test you have employed and explain your answer. Show how the relevant test statistic was calculated_ Indicate value for the appropriate test and explain the meaning of the value [60%]



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Two fuel additives are being tested to determine their effect on gas mileage. Seven cars were tested with additive 1 and nine cars were tested with additive $2 .$ The following data show the miles per gallon obtained with the two additives. Use $\alpha=.05$ and the MWW test to see whether there is a significant difference in gasoline mileage for the two additives. $\begin{array}{cc}\text { Additive 1 } & \text { Additive 2 } \\ 17.3 & 18.7 \\ 18.4 & 17.8 \\ 19.1 & 21.3 \\ 16.7 & 21.0 \\ 18.2 & 22.1 \\ 18.6 & 18.7 \\ 17.5 & 19.8 \\ & 20.7 \\ & 20.2\end{array}$

Okay, we're looking at gasoline additives. I mean, difference is your .66. The standard deviation of the differences is your .443 giving us a T statistic of 4714 Our hypothesis are that the mean differences are going to be zero. Our alternative is that the mean difference is going to be greater than zero. Since we're thinking that additives perform better. When we find out the p value, we find out that it is less than 1%. Therefore, we reject the null hypothesis in favor of the alternative. The gasoline additives are helpful or add more gas mileage to be more specific. Next, we will apply a pool T test The average for the first one is 17.21 and as follows for the rest, the next thing that we need to do is pool these standard deviations denoted as sp which is going to be this 897 Surprisingly very nice average. Okay. Mhm. And the next part we are going to do is find out that the statistic which is looking a lot like the previous one, is going to be the difference of the two means divided by the pool standard deviation times the square root of the some of the reciprocal standard deviations or sample sizes. Um So what that's gonna look like is this? Yeah. All right. Key Value of .1, Next thing that we need to do is calculate the degrees of freedom, which is going to be the some of the sample sizes and one plus and 2 -2. So it's gonna be 10 plus, 10 -2 equals 18. And then we have 18° of freedom. So going down the table, we see that the P value is greater than 10%, uh which is greater than 5%. Therefore, we failed to reject the null hypothesis, but this is because the two samples are dependent. We're looking at adding a fuel additive and adding another one. So what this means is that we weren't supposed to use a pool T test because pool T tests are only for two independent populations and these weren't, so it wasn't appropriate to do a pool T test in this situation.

Question. We have efficiency of the auto cycle is equal to one minus r. To the power one minus gamma. Where gamma is the idea better coefficient. And for the uh Fuel here we have gamma equals to 1.4. Okay now we have four types of different fuels. So we have to calculate the efficiency for each so we can write that efficiency maximum for the uh octane number 91 this will be equal to one minus R. To the power one minus gamma for the 91. Okay, so we have values from the table so we can substitute one minus 8.5 to the power 1 -1.4. So from here after solving we get efficiency maximum for the octane number 91 equals to 0.5752. Okay. And in the similar way we can calculate the remaining value. So efficiency for the octane number 93 it will be one minus r. To the power one minus gamma one minus gamma. So substituting values so we will get one minus 9.0 to the power one minus 1.4. So from here we get efficiency for the octane number 93 that is equal to 0.5848 And next for the 95. So efficiency maximum for the 95 it will be 1 -195 to the power one minus comma. So we get one minus R which is 9.8 to the power one minus 1.4. So from here we get maximum efficiency for 95 octane number is equal to 0.594 5987. Okay And maximum efficiency for the octane number 97, it will be same this value. Okay, so substituting values so we get 1 -197 which is 10.5 to the power one minus 1.4. So from here after solving we get efficiency maximum for the octane number 97. This comes out to be 0.6096 Okay so these are the different answers for this question. Okay this this answer and this is another answer. Okay next we have to calculate next, we have to calculate the uh changing efficiency. So percentage increase in efficiency percentage increase in efficiency to this will be equal to uh efficiency maximum 40 97. That is 0.6. G 096 minus efficiency maximum 40 91. That is 0.5752 They were by 0.5752 multiplied by 100%. Okay so from here after solving we get percentage increase in the epicentre. See we get 66.0%. Okay, so this much of efficiency has been increased when we go from octane number 91-97. Okay.

So this question we are given some data about small cars and were basically given their MPG reliability and safety. So these are the three X variables and were given the Y variable, which is price, and were asked to determine the multiple regression equation four price. So let's go ahead and do that. So our input wide range is basically price. So that goes up until to sell 21. We have he want to If 21 here for our input Wire ridge for our input X range. We start at B one and we will end at B 21 because we have the three cold P, C and D keep our confidence level at 99% are output range. We are going to put it over here, so we have it at 8. 24. We make sure we have our wide range and our X range our output and we click okay to get our multiple linear regression equation. So we have all of our regression statistics off here. So we see our r squared 0.72 which is all right then going on. So we have our coefficients here for the three values. So basically, let's use thes coefficients on Get Our multiple in Your regression equations are first. It's for mpg and reliability and then safety. So right me close to intercept minus 2 81 and C ci for us to or seven or the liability yes has been 700 times u p we have prices equals two minus check. Our intercept crisis equals to 18861 minus to 81 times x one plus 27 times x two plus 1700 times extreme. So we basically have power equation over here. Yes, we're part is now let's move on to Part B now in part, we were asked to use the F test to determine the overall significance of the relationship. So we have our f statistic over here. So I zahra a statistic r p value this 0.41 So that's pretty small. Mhm. And so since the p value off point or one is less than 0.45 relationship, they significant and one or more off the variables. Uh huh. Not people to thio. There is a significant relationship between why and at least one or more off the variables, which is what part of being and we have. Statistics on the P value is telling us now moving on to part Seaver as to use the team tests to determine the significance off each variable. So let's do that. So we have each variables. We have mpg reliability and safety and were asked to use the teachers to determine the significance of each of these variables at 0.45 So we see that mpg and safety are less than 0.5 and so therefore they're significant. But reliability is not significant, so let's go ahead and starting. So for MPT, you know you just left standpoint or five. Is this significant for reliability? I love you. Daddy needs into four, which is more than point or fight. So it's not significant. And then, for our last variable safety, very small pre values. Please, Please Do you have a new leach to time standard about a minus bi sport, which speaks. Can you suggest that and soup? We have our answer to part C to variable significant one. Not significant now for party, we are told toe first to remove any independent variable that is not significant from the equation. So let's do that. Okay, so we're going to have to remove reliability from the equation. So let's go ahead and do that first. So now we have re motors liability from power equation, and that's two linear regression. So we have the wide range, the X Range 99% and we get our summary output here. So we see we see our r squared and there we have it. So we have our coefficients for the intercept mpg and 60. So let's write our linear regression equations. We have 25 deep crisis people's through the intercept when we have some PG and safety until there's some differences. Flight differences When politicians between the party and part team, they're pretty similar and then were asked in 14 after writing the recommended regression equation to compare the R squared 44 so are our squared for party was 0.722 adjusted. Our square was 0.67 So it's right that right now are square or party with just two variables on adjusted R squared 0.69 point 7.66 So we can basically conclude that our differences in our square were very I mean, we're very minimal or very little even after removed after removing non significant variable so we can include that the variable that's not count for much off variability in the data and for two significant variables account for most off variability. So basically, because they r squared values were pretty similar or even when we removed the non significant variables, we basically can see that the two significant variables are what account for most of the variability in the data. And the non significant variable really does not contribute much to the equation. So that's our conclusion, and this is the answer for 25 party through people.

Her solution for the question is, they're giving that volume of gasoline. Yeah, Okay. Equal to 2.8 Zito. Air bridge and hitting value. Right. Mhm equals toe three point 25 into 10 to the power four killer Jude Borrell. So we know that formula. Total heat supplied equal toe volume off gasoline into heating value toe So total he supplied well, equal toe volume off gasoline, which is 2.80 our parrot. Mm. Into uh huh. Heating value, which is three point 25 into 10 to the power four Clue, dude, but and yeah, Mhm. Yeah, right, right. This is it. Yeah. So by this. So this cutting by simplifying this Finns get 9.1 zero. Yeah, into 10 to re power four. Hello, Jewell. But ah, so for next next step work done by Indian for one Are, um work done by Indian. Yeah, for one. Are And you. We know that worked on equal toe heel supplied in 2 35 100 work done equal toe. He'd supplied into 30 by 100. So by solving this, we get worked on equal toe to point 73 in tow, 10 to the power four. Kill a jewel. Mhm. Yeah, No. For the next step, power produced by Indian power produced. Bye Indian. Yeah, This will be power delivered equal toe power. Yeah. Deliver equal toe work. Done by a time work done divided by time By putting the value, we get 2.73 into 10 to the power four Kill a jewel per are divided by one are by solving this we get by simplifying this We'd yet power. Yeah. Deliver equal to seven point 58 TV kill. Oh, what? Right? Yeah, yeah. No, um, power produced in horsepower now for power produced. Yeah, and horsepower. Mhm. No. This will be equal to power. Deliver. I'm cover to 7.58 Titi, actually, Globe art into one 0.3 for one ha Spa divided by Chlo. What? And hair we get 10.168 HB found, sir. Thank you.


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