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Statistics Experiment

Transcript: by, Lauren Mora and Nancy Huerta The p-value is equal to the probablitity that a t-score having 138 degrees of freedom is more extreme than our t-value of 6.77. Since the p-value is low, we reject the null hypothesis and thus conclude that there is statistically significant evidence to conclude that nicotine enourages mice to consume more water adn is addictive. We set up identical environments for both mice with medicine measuring cups as water cups for the mice at four similar times every day for 20 days. The cups were glued to the bottoms of the two houses to avoid any outliers that might result from the water getting spilled onto the mice’s environment. We then crushed one tablet of nicotine water into one of the medicine cups to avoid ant side water consumed by both mice throughout the 20 days that we carried out our experiment; we measured the water consumption in millimeters. We did not however, avoid the bias of food consumption of the mice since they ate at different rates and we chose to prioritize keeping them alive for as long as possible. We also did not avoid the bias of the mouse that dies two days before our experimental design was completed, not the paper shredding that fell into the water, thus adding to the water levels of the cups when needed. We are confident that our samples match our proportion because we took the necessary precautions to avoid bias. Variable Graphs: 4. two identical containers Can mice become Addicted to Nicotine? 6. Labeled containers What our Experiment Consisted of: 1. measured the amount of liquid consumed by each container and each mouse What we used: Linear model for Nicotene Consumption 2.took the measurements 4 times a day for over 20 days. mouse 2= variable, nicotene and water 3.determined if the Nicotene mouse was consuming more and more of that water. more Nicotene than water about half and half What we concluded: In our experiment, we received two subjects through randomization where neither the mice nor the pet store employee was aware they would be used for an experiment. This gave us a simply random sample of two mice through double blinding. We randomly assigned one mouse to be part of our control group by marking whichever mouse was on top with a blue marker. This prevented any biases that may have resulted from choosing one mouse over the other to consume the nicotine water. How We collected our data 3. medicine cups to measure H2O & Nicotene water Control mouse 1= control, only water 2. Nicotene pills, "Nicorette" 1. Two identical feeder mice That mice can infact become addicted to nicotine, but is not ideal because mice are not like humans and can potentially kill the mouse. graphs shows a positive increase but the values are not consistant 5. Food to supply the mice with -We wanted to conclude if their was statistical evidence to prove if mice could become addicted to Nicotene -we measured the amount of water each mice drank from each water container, if the mouse that had the nicotene progressively drank the nicotene water over the plain water it would reject our null hypothesis and conclude that a mouse could become addicted.

AP Statistics Experiment

Transcript: By: Alyssa, Morgan and Katherine Do: test stat: z=(p1-p2)-0/(sqr.rt.)[(pc(1-pc)/n1)+(pc(1-pc)/n2)] z=(.48-.129)-0/(sqr.rt)[(.286(.714)/25)+(.286(.714)/31)] =2.89 pc= (12+4)/(25+31)=.286 p-value=normalcdf(2.89,E99)=.001925 Conclude: Since our p-value is less than our sig. level (0.5) we will reject Ho. There is statistically significant evidence that the true proportion of females who would correctly identify the name brand soda is greater than the true proportion of males who would correctly identify the name brand soda. This supports our hypothesis. State: We want to create a 95% confidence interval to estimate the true proportion of students who would correctly identify the name- brand soda. Plan: Create a 1 sample z interval for proportions if conditions are met. Random: subjects were randomly assigned to treatments/ soda flavors(calculator random int.) Independent: each student's guess was independent of each others. 56< 10% of the total population of students at Sun Prairie High School Approx. Normal: n(p)>10 56(15/56)=16>10 n(1-p)>10 56(40/56)=40>10 Females were more than 3.5x as likely to correctly identify the name- brand soda than males. State: Ho: p1-p2=0 Ha: p1- p2> 0 sig level= .05 p1= the true proportion of female students who would correctly identify the name brand sodas p2= the true proportion of male students who would correctly identify the name brand sodas. Plan: Run a 2 sample z test for proportions if conditions are met. Random: Both males and females were randomly assigned to the sodas they would sample. Independent: We sampled without replacement. Each male and female's guesses were independent of each other. 31 and 25 are <10% of the population of male and female students at SPHS. Approx. Normal: n1p1>10/25(12/25)=12>10 n1(1-p1)>10/25(13/25)=13>10 n2p2>10/31(4/31)=4<10 n2(1-p2)>10/31(26/31)=26>10 Question: How easy is it to tell the difference between name brand and off brand soda 1)Will our subjects be able to differentiate between the name brand sodas and the off- brand sodas? 2)Will males or females be more likely to correctly identify the name brand soda? 3)Will people be more likely to start with the soda type they like most or another type of soda? Why this topic?: We wanted to do something different and we new that if we gave the subjects food it would be easier to get people to participate We poured 3 different types of sodas in identical Dixie cups and labeled each pair A and B. We randomly selected which cup, cup A or B, the name brand soda was poured into using the (random number generator on the) calculator. This bar graph shows that the proportion of students who were unable to identify the name brand soda was much larger (almost 2.5X larger!) than the proportion of student who were able to correctly identify the name brand soda. Conclusion Hypothesis #1 Introduction Hypothesis #1 Cont: In conclusion, through our experiment we have been able to confirm that the majority of students at SPHS cannot differentiate between the name-brand and off-brand sodas, and more female students than males students can correctly identify the name-brand soda. We cannot confirm, however, that the majority of students would start with their favorite type of soda. We then set the different cups (4 in all) in front of our subjects and asked them to sample all of them, starting with which ever one they would like. As they sampled the soda they filled out questionnaires that asked them to identify which cup (A or B) contained the name brand soda. We also asked for their gender, their favorite type of soda, and which soda they started with first. Hypothesis #2 Cont: Hypothesis #3 Cont: Do: p(+/-) z*(sqr.rt.)[p(1-p)/n] (.612)(+/-)1.645*(sqr.rt)[.612(.388)/49]= (.4975, .7265) p=(30/49)=.612 Conclude: We are 95% confident that the interval from .4975 to .7265 captures the true population proportion of the number of students at SPHS who would start with their favorite type of soda. Since the interval contains values below .5 and above .5, we cannot conclude that more students would start with their favorite soda than those who would not. Hypothesis #1: State: We want to create a 95% confidence interval for the true proportion of students at SPHS who would start with their favorite soda in our experiment. Plan: create a 1-sample z interval for proportions if conditions are met. Random: subjects were randomly assigned to two types of soda. Independent: each students guess was independent of the others 56<10% population of students at SPHS Approx. normal: np>10/49(30/49)=30>10 n(1-p)>10/49(19/49)=19>10 How we will analyze our data: 1. One sample z interval for proportions P1= true proportion of students who would correctly identify the name brand soda 2. Two sample z test for proportions P1= the proportions of females who identified the name brand soda correctly P2= the proportion of males who identified the name brand soda correctly 3. One sample z interval for proportions P1= the proportion of students

Statistics Experiment

Transcript: Experimental Design Matched pair experimental design better compare results of a junior taking a SAT reading section with and that without a highlighter. controls: two passages equal in difficulty; subjects in the same grade Controlling lurking variables: same room, same time, and allowing the same amount of time. randomization: assigning the subjects numbers and randomly assigning one of each pair to the experimental group allowed proper replication because subjects were pretested then paired. These pairs were then compared statistically through the analysis of the scores of their second passages. This makes the experimental procedure more specific and consistent as it can be repeated in an identical and replicate manner without variation which contributes to the accuracy of the data and results Convenient sample, so: possible bias because the students are in the same class, so their scores may be more similar to each other than if the population was random, underestimating the difference using a highlighter makes for a typical junior. because they are taking a SAT prep class, they may perform better in general, therefore underestimating the effects of using a highlighter. Elements to to minimize error: We used scores from the pre-test to pair individuals of similar skill sets together for comparison We gave all students the same exam to avoid inconsistencies due to different difficulty levels We also tested pairs at the same time to avoid inconsistencies in performance due to variations in time of day. We controlled time allowed for testing to avoid better scores due to more time. To further minimize error in our results, we could have controlled environment and highlighter color. Population: Northview juniors Sampling: convenient sample of 20 juniors in a zero period SAT class. Pretested without a highlighter, scored, and matched randomly assigned one person in each matched pair to use a highlighter on a second, different reading section and the other to do the second section without the highlighter. Ideally, we would assign all 400 Northview juniors a number, select 20 unique juniors, pretest and match, and retest matched pairs with pretest scores collected scores from juniors from post-test (with and without highlighter) The participants did not know if they were using highlighter or not before hand. In the 10 pairs that were tested, most did better when they used the highlighter with an exception of few. For trials 1,2,3,8,9 and 10, the results were better with the highlighter and for trials 4, 5, 6 and 7, the ones that did not use a highlighter did better on the test. Out of 10 trials, 6 did better with the highlighter. RESULTS Calculations Conclusion cont... Generally, the use of a highlighter resulted in a higher score We expected this result, since highlighters emphasize key facts and ideas In 6/10 of the pairs, the individual with the highlighter got a higher score In only 3/10 of the pairs, the individual without the highlighter score higher 1/10 of the pairs scored the same. Possible sources of error include: bias (convenience sampling and the preconcieved notions of subjects) lurking variables (time taken, testing environment, motivation, etc.) placebo effect, since the subject knew whether he or she was receiving the treatment (highlighter) or not, skews performance. Purpose Conclusion and Summary The Graph of the scores of subjects who used highlighters is skewed left, so mostly high scores, whereas the graph of the scores of subject who did not use highlighters is skewed right, with mostly low scores. The mean (90%) and median (91.66%) of those who used a highlighter were higher than the mean (81.67%) and median (83.33%) of those who did not use highlighters. There were two outliers in the highlighter graph, 58.33% and 75%, pulling the average down, and there were no outliers in the non-highlighter graph. The standard deviation (0.135) and IQR(0.3333) for the highlighter graph are greater than the standard deviation (0.117) and IQR (0.2499) of the non-highlighter graph, so the spread for the non-highlighter scores was smaller. Sources of Bias The Highlight Graphs Subjects Comparison RESULTS To determine if being allowed to use a highlighter would enable Northview juniors to perform better on the SAT multiple choice reading passage section, as opposed to not having a highlighter.

Statistics Experiment

Transcript: M A I A S T A T I S T I C S E X P E R I M E N T / GRAPH / ---------- P P D A C / PPDAC / I wonder if there is a relationship between the 'height' and 'how fast the students in 9Kiwi can run'? PROBLEM ------------ PROBLEM PLAN PLAN - Firstly we are going to ask the students to get into peers. - They will need to have a stopwatch between them both to time eachother run. - The partners will decide on who will run first and second. - Aproximetly a day prior to the experiment we will send an email out, reminding the class to bring appropriate clothes if they decide not to run in uniform. - To make it fair, we will have everyone wearing barefeet. - In order to get a reasonable result, we will have the students run 50m (this will be simple to measure as they can run from the centre line of the rugby field to the end). - Everyone running will start at the same time. - One partner sprints their fastest while the other times at the opposite end. - Afterwards the runner will share their time with us and we will record it on a google sheet. - The peer will then swap roles. - We will not need to measure everyones height as we will take all of that info from a experiment that has already been done. - Finally we will paste all of the info from the google sheet into NZGrapher and observe for any relationships. DATA DATA GOOGLE SHEET THIS IS OUR GOOGLE SHEET IN WHICH WE RECORDED ALL OF OUR INFO ON :) TREND ASSOCIATION STRENGTH SCATTER OUTLIER GAPS/GROUPS ANALYSIS I have observed the final result and noticed that as the persons height increases their sprinting speed remains the same, in some people’s relationship it actually decreases. Obviously there is some assumptions to this experiment and these form our 5 outliers. TREND TREND This scatter graph consists of a negative/neutral relationship. ASSOCIATION ASSOCIATION This graph has a moderate strength. Although there is not a bold/obvious connection with all of the data points, there is a connection/relationship. STRENGTH STRENGTH I think that this diagram has a neutral scatter because I believe the data points are at an in between level, as they are not spread hugely apart however they are not all in the exact same area. SCATTER SCATTER 1. This male is 148cm, the shortest in the class. Although he is one of the shortest he sprinted 50m in 7.5 seconds, which is indeed one of the fastest times in the class. We classify this as an outlier as the height and speed do not match. 2. This female is 154cm however her sprinting speed was 12 seconds. For this students height, this is not a fast time. 3. This male is 167cm tall, his height is on the taller scale of the class. The speed time this student was 11seconds. As we can tell that this male is quite tall, his time does not match. 4. This is a peer of 2 outliers, one female and one male. They are both extremley tall, possibly classified as the tallest in the class. They both hold an average running time of 10 seconds for a 50m sprint. There height does not relate so this counts as our fourth outlier. 5. This male's height is 176cm and his sprinting time is 7.5 seconds. Unlike the others, this is the only outlier that has a relationship/makes sense with the speed and height. OUTLIER OUTLIER 5 outliers As we can sight, the are 2 larger gorups on this graph. There is also another smaller group, that is only made up of 2 data points. I believe that we could classify this smaller set as a group, as they are placed in the middle of the additional groups and the height and speed relates. The data points on this graph that are not contained in a group are the 5 outliers. These are associated as the gaps on my graph because the height and speed do not match. GAPS/GROUPS GAPS/GROUPS In conclusion, after completing this investigation between 9kiwis height and how fast they can sprint in 50m, we found that there's not any relationships. In fact, a few of our fastest runners were the shortest in the class. We noticed that some students were not ast fast as they should be for their height, especially a variety of the taller ones. A couple of data points would dissagre with this conclusion as the height matched the time occasionly, although these were very irregular points. CONCLUSION CONCLUSION - I believe that one of the downsides to this investigation would be that so many people within our class were not able to participate in the sprint. This affected our results as it's better to have as many people as you can when doing statistics experiments. Would of been very fortunate if everyone could join in. - It is likely that not all of our results were fair and accurate because of the way we timed the students. We all agreed that if we were to do this again, we would time the students individually. Unfortunately we were not able to do this as we needed to form an idea that would run swiftly for our class, Mr A and our experiment. As this would of taken up much of the students time measuring one by one and it was inconvenient taking them out of

Statistics Experiment

Transcript: P = 10/18=.556 P = 11/19=.579 P = P - P = 0.02339 standard deviation (P ) = sq([(21/37)(16/37)]/18 + [(21/37)(16/37)]/19) =0.16295051 z= (statistic - parameter)/standard deviation z= (0.02339 - 0)/0.16295 z= .1435 X Does a person's gender affect the way people respond to them in a time of crisis? X Hypothesis: > 2 2 H0: P1 = P2 Ha: P1 < P2 P1= proportion of males that were helped by strangers P2= proportion of females that were helped by strangers P1 = 10/18 P2 = 11/19 2 Prop Z test with significance level of 0.05 > p = 0 Riya Jain & Sanjana Palepu P - Value Random: We randomly approached people asking for their help Data: 10) No 11) Yes 12) Yes 13) Yes 14) No 15) No 16) No 17) Yes 18) No CONCLUSION np ≥ 10 18(10/18) ≥ 10 10 ≥ 10 np ≥ 10 19(11/19) ≥ 10 11 ≥ 10 Thank You! 1) Yes 2) No 3) Yes 4) Yes 5) No 6) Yes 7) No 8) Yes 9) Yes p = 0.02339 Statistics Experiment nq ≥ 10 18(8/18) ≥ 10 8 ≥ 10 nq ≥ 10 19(8/19) ≥ 10 8 ≥ 10 d Males 2 It is plausible that there is no difference between the true population proportions of males and females since there is insufficient evidence for proportion of females helped by strangers being greater than proportion of males helped by strangers. > > d 1 Normal: We proceed with caution > 1 Assuming that there is no difference in the true population proportion of males and females, the probability of getting a sample at least as extreme as observed due to natural sample to sample variability is .4429. Females 10) No 11) No 12) Yes 13) Yes 14) No 15) No 16) Yes 17) Yes 18) Yes 19) No 2 Parameter: Independence: Samples independent since comparative randomized experiment 1) No 2) Yes 3) Yes 4) Yes 5) No 6) Yes 7) N0 8) Yes 9) Yes Our P value = 0.4429 is greater than the significance level = .05 Statistic: Therefore, we fail to reject the null hypothesis P value : P( p = 0.02339 l p = 0) = P ( z > .1435) = .4429 > 2 Proportion Z test One girl was assigned the task of randomly asking people walking around at spectrum to borrow their phone because "her phone died" or she "left it at home" and she "needed to call her parents" The number of people who lent their phone to the girl were recorded and this process was videotaped. This experiment was repeated again with another girl, and two different boys. Method > 1 > Question: > 1 Conclusion Conditions:

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