Data Analysis Chapter Analysis

Data Analysis Chapter AnalysisPart OneBased on my NTU aimrname (N0687816), my data set is (0,6,8,7,8,1,6)Section A) Forming a 99% confidence interval for my data set Our confidence interval is We can in that respectfore arrange with 99% confidence that the mean number of tattoos per student for the population of all students at NTU is between 0.54 and 9.74Using Minitab for a 99% confidence interval for data set (0,0,0,1,3,3,7)Section B) Looking for evidence at the 97% confidence direct of a difference between the samplesSample 1 (0,6,8,7,8,1,6)Sample 2 (0,0,0,1,3,3,7)Sample sizesSample meansSample variances I am taboolet to use a two-sample T test to crumble this data as there are two small samples formed from data that is not paired.We can say with 97% confidence that there is no difference between the two samples.Using MinitabSection C) Testing data from trialing a new inhaler individual 1Person 2Person 3Person 4Person 5Person 6Person 7Before0687816After0001337To analyse th is data, I will use a paired T-test as there are two sets of data for the same group of people (before and by and by using an inhaler). It is also unknown if the data is normally distributed and the sample is small which are both other factors which suggest the use of a T test. This test could be unmatched or two tailed depending on whether you were looking for an improvement/reduction or a general change. In this case, however, we want the inhalers to have amend the peoples lung function so we will do a one tailed test.Null hypothesis Alternative hypothesis. (The data is for recovery time in seconds so a reduction in the mean recovery time shows an improvement in lung function).Decision Rule Performing the testLet So in that location is not a specified confidence interval so I will use a 95% confidence interval so thereof We can therefore say with 95% confidence that the inhaler did improve the lung function of the people who used it.Testing the Manufacturers ClaimI am goin g to use a one tailed hypothesis test. This is because it does not matter if the inhaler improves lung function in over 80% of cases, only if it does not prepare this claim. I will take to be that and to be that .The lung function recovery time reduced in intravenous feeding of the seven trials so 4 events out of 7 trials, leading to and Part TwoSection A) The Lady Tasting Tea ExperimentThe lady tasting tea look into was a statistical experiment conducted by Ronald Fisher. As explained in The lady tasting tea experiment (Winkler, 2015), a lady claimed she could tell whether milk or tea was poured initiative in a cup of tea she tasted. Ronald Fishers book The Design of Experiments (see Winkler, 2015) outlined the ideas behind this testIt consists in mixing octad cups of tea, four in one way and four in the other, and presenting them to the subject for judgement in a random order. The subject has been told in advance that she will be asked to taste eight cups, that these sha ll be four of each kind Fisher, 1935.According to Imai (2016), Fisher introduces the idea of a null hypothesis, which in this case, is the idea that the woman is guessing and cannot actually manage between the cups. Fisher then used the ladys answers to work out the likelihood of her getting this result whilst guessing. From this, he found that there were 70 ways to pick 4 cups out of 8 and that from these, there was 1 way of getting none and four recognise, 16 ways of getting one and three correct and 36 ways of getting two correct, as shown by Inglis-Arkell (2015).Although pioneering, however, the test itself was not powerful. As explained by Stark (2010), the small sample size caused the hazard of her guessing randomly only coming out less than 0.05 (the condition required to reject the null hypothesis) if she got a perfect score. This is because guessing all four correctly carried a luck of whereas guessing three out of four correctly carried a probability of . This issue would have been reduced with a very much bigger sample size.For another mathematical example, we will look at the following questionSuppose the lady samples 10 cups of tea, among which 5 had the teapoured first and 5 had the milk poured first.a. What is the probability she correctly identifies all five cups which had the tea poured first? Sloughter, 2006.Following the logic displayed by Stark (2010) for the lady tasting tea problem, there would be only 1 way of choosing all five correctly. Using the formula (Simmons, 2016), we get ways of choosing five cups of tea out of the ten. This means that the probability of getting all five correct is .As stated by Inglis-Arkell (2015), the number of cups that the lady guessed correctly is unknown. Despite this, the lady tasting tea experiment is still extremely influential and led to Ronald Fisher being praised for his book The Design of Experiments due to how clearly he explained why randomisation is important and how he decided what wo uld be acceptable evidence to accept or reject a statement.Reference ListImai, K., 2013. Statistical Hypothesis Tests online. Princeton University. Available at http//imai.princeton.edu/ belief/files/tests.pdf Accessed 9th January 2017.Inglis-Arkell, E., 2015. How A Tea Party Turned Into A Scientific Legend online. Io9. Available at http//io9.gizmodo.com/how-a-tea-party-turned-into-a-scientific-legend-1706697488 Accessed 9th December 2016.Simmons, B., 2016. Combination Formula online. Mathwords. Available at http//www.mathwords.com/c/combination_formula.htm Accessed 9th January 2017.Sloughter, D., 2006. Mathematics of a Lady Tasting Tea online. Furman University. Available at http//math.furman.edu/dcs/courses/math15/lectures/lecture-19.pdf Accessed 9th December 2016.Stark, P., 2010. StichiGui online. Available at https//www.stat.berkeley.edu/stark/Teach/S240/Notes/ch3.htm Accessed 9th January 2017.Winkler, A. 2015. The lady tasting tea experiment online. Brainder. Available at https //brainder.org/2015/08/23/the-lady-tasting-tea-and-fishers-exact-test/ Accessed 5th December 2016.Declaration1. I am aware of the Universitys rules on plagiarism and collusion and I discover that, if I am found to have broken these rules, it will be treated as Academic Misconduct and dealt with accordingly. I understand that if I lead this piece of work to another student and they copy all or part of it, either with or without my knowledge or permission, I shall be discredited of collusion.2. In submitting this work I confirm that I am aware of, and am abiding by, the Universitys expectations for proof-reading.3. 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