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1 Exercise 2 8 page 57 of course text 1 a 3 5 6 7 9 b 3 5 6 7 20 Explanation Distribution 1 2 have the same median six but distribution two has a larger IQR because the distribution of example 2 is larger than distribution one We can infer that the data is more spread out but then distribution to the data set is more than likely due to the outlier 20 which is a very large collection compared to part A s outlier 2 a 3 5 6 7 9 b 3 5 7 8 9 Explanation After calculation the median of part A is one less than Part B part A s IQRS is 5 less than the IQR of Part B in this case both distributions can be deemed to be di erent Part b data that is more spread out or part A having a less IQR could recommend a middle cluster 3 a 1 2 3 4 5 b 6 7 8 9 10 Part A s median is comparatively low compared to the meaning of Part B although the medians are di erent they do share the same IQR 4 a 0 10 50 60 100 b 0 100 500 600 1000 Both have extreme di erences in medians as well as yours due to the vast large associated with each disturbance 2 Exercise 2 22 page 69 of course text a What percent of these Tampa FL voters identify themselves as conservatives 372 910 40 879 b What percent of these Tampa FL voters are in favor of the citizenship option 278 910 30 549 c What percent of these Tampa FL voters identify themselves as conservatives and are in favor of the citizenship option 57 910 6 264 d What percent of these Tampa FL voters who identify themselves as conservatives are also in favor of the citizenship option What percent of moderates share this view What percent of liberals share this view 57 372 15 323 the percentage of moderates that share this view is 120 363 33 058 the percentage of liberals is 101 175 57 714 e Do political ideology and views on immigration appear to be independent Explain your reasoning No political beliefs and ideas on immigration are not separate But only 6 of conservatives want the citizenship choice On the other hand 33 of moderates and 58 of liberals want it So conservatives and liberals have very di erent ideas about immigration 3 Exercise 2 26 page 76 of course text a Based on the mosaic plot is survival independent of whether or not the patient got a transplant Explain your reasoning No it looks like the patient s chance of life depends on whether or not they got a transplant The dead area in the control group looks a lot taller than the treatment group s but the survival parts look the opposite way It is known that there are a lot more people in the treatment group than in the control group This could make it hard to tell if the treatment has a big e ect on the life rate The mosaic plot indicates that a greater proportion of the treatment group survived than the control group This suggests a dependent relationship between the transplant and survival b What do the box plots below suggest about the e cacy e ectiveness of the heart transplant treatment The heart transplant treatment signi cantly increases the survival time days for patients it appears all measurements of the data e g Q1 median etc are signi cantly better for the treatment group than the control group The median of the treatment group is nearly 1 year while the control group is very very low Even the Q1 of the treatment group is higher than the Q3 of the control group nevermind how much higher Q3 of the treatment group is The boxplots suggest that the transplant treatment is e ective at buying the patient additional time c What proportion of patients in the treatment group and what proportion of patients in the control group Died 88 of the patients in the control group died by the end of the study and 65 of the patients in the treatment group died by the end of the study d One approach for investigating whether or not the treatment is e ective is to use a randomization technique What are the claims being tested Having a stent and survival are independant Any relationship is due to chance H A Having a stent and survival are dependent Any increase in survival rates is due to the stent treatment Independent Model The transplant treatment has no e ect on survival The observed higher survival rate was due to chance Alternative model The transplant treatment has an e ect on patient survival The observed higher survival rate was not due to chance The paragraph below describes the set up for such approach if we were to do it without using statistical software Fill in the blanks with a number or phrase whichever is appropriate We write alive on 28 cards representing patients who were alive at the end of study and dead on 75 cards representing patients who were not Then we shu e these cards and split them into two groups one group of size 69 representing treatment and another group of size 34 representing control We calculate the di erence between the proportion of dead cards in the treatment and control groups treatment control and record this value We repeat this 100 times to build a distribution centered at 0 Lastly we calculate the fraction of simulations where the simulated di erences in proportions are less than 0 230179 If this fraction is low we conclude that it is unlikely to have observed an outcome by chance and that the null hypothesis should be rejected in favor of the alternative Ii What do the simulation results shown below suggest about the e ectiveness of the transplant pro gram We can see from the simulation results above that the di erence in our original proportion roughly 0 257 is very unique suggesting that this did not occur by chance We can reject the null hypothesis as there is strong evidence that the experimental heart transplant does increase lifespan 4 Exercise 2 34 page 78 of course text a What features of the distribution are apparent in the histogram and not the box plot What features are apparent in the box plot but not in the histogram In the histogram the two modes are more visible The distribution has two extremes It s easier to gure out where the mode is This is because the Histogram shows that the distribution has two peaks while the box plot does not Based on this information the right answer is that the distribution is bimodal and it s easier to nd the mode In the box plot the outliers and median value are more apparent It is clear where the center is located It s easier to nd possible outliers This is because the box plot makes it easy to see which values …

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