Statistical Analysis and Hypothesis Testing: A Comprehensive Study on Data Interpretation, Probabilities, and Confidence Intervals

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Statistical Analysis and Hypothesis Testing: A Comprehensive Study on DataInterpretation, Probabilities, and Confidence IntervalsIn this assignment you may use your book, your notes and your calculator. SHOW YOURWORK WHERE STATED TO DO SO TORECEIVE FULL CREDIT. Round all decimalanswers to 4 decimal places.1.The population of the City of Baltimore is 622,104 (as of July 1, 2013).MayorRawlings-Blake would like a survey of the residents of Baltimore to determine if they aresatisfied with how Monday’s riots were handled.How could a survey be developed thatis unbiased and addresses a representative sample of the population?Solution:A survey should be developed which is unbiased and sample should be taken usingsimple random sampling method. In simple random sampling, a sample is selectedrandomly from population of the City of Baltimore consisting of 622,104 people. Here,each member of the population has equal and independent chance of being selected in thesample. An unbiased survey should be conducted such that respondents answer thesurvey reflecting their true beliefs about Monday’s riots.2.What is the difference between qualitative and quantitative data?Give an example ofeach.Solution:Categorical variables come under the category of Qualitative data. While data which canbe measured on numeric scale that is they are represented as numbers comes under thecategory of quantitative data.For example,genderis qualitative data which can becategorized asmale or a female.And,weightofpersonsis a quantitative data which canberepresentedasnumericlike30, 45, 65, 80, 110 Kg.Consider the data below for questions 3--4.

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3.What number best represents the 25th percentile?Solution:904.Prove or disprove theexistence of outliers.Solution:There are no outlierspresent in the data, as there are no individual points on Box plot.6.Determine the mean, median and mode for the data below.Which measure of centraltendencybestrepresents the data? Provide reasoning supporting your answer.Number of Days Absent per Student, Mr. Steven’s 6thgrade class751230513125063811014911236011Solution:Mean = sum of all observations / total number of observations= 155/24= 6.4583Formedian, first of all arrange the data in the descending order which is shown below.00001112334555

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6679111112121338I know that, when n = even,Median = average of (n/2)thand((n/2) + 1)thobservationHere,n = 24,thus median = average of24/2th and ((24/2)+1)th observation=average of 12thand 13thobservation=(5+5)/2=10/2=5Mode is the observation occurring maximum number of times. Here is 0is occurring 4times, which isthe maximum frequency here. Thus, mode = 0Here 38 is an outlier,And in presence of outliers, Median is preferredover mode and mean.Thus,median is the best measure of central tendency.7.Jason and Mary took an entrance exam with a certain company. Jason scored a 76%. Hiscohort’s average was 80% with a standard deviation of 5%. Mary also scored a 76%.Her cohort’s average was an 83% with a standard deviation of 8%.Determine a z-scorefor each person and compare their scores using z-scores. SHOW YOUR WORKSolution:For Jason,X = 0.76, average = 0.80 and standard deviation = 0.05.Z score = (X-mean)/s.d.= (0.76-0.80)/0.05=-0.8For Mary,X =0.76, average = 0.83 and standard deviation = 0.08.Z score = (X-mean)/s.d.=(0.76-0.83)/0.08=-0.875

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Jason’s score is 0.8standard deviationsbelow the mean.Mary’s score is 0.875standard deviationbelow the mean.8.A gumball machine contains 10 blue, 5 pink, 5 orange, 16 yellow and 14 white gumballs.What is the probability that a child receives a yellow followed by a white? (Noreplacement).SHOW YOUR WORKSolution:Blue = 10Pink = 5Orange = 5Yellow = 16White = 14Total = 50Thus, P(Yellow) = (16/50)P(White) = (14/49)Required probability =P(Yellow)P(White)= (16/50)*(14/49)=0.09149.Find the probability of rolling two dice and getting a sum of eight. SHOW/EXPLAINYOUR WORKSolution:Sample spaceon rolling 2 dice is:{ (1,1), (1,2,), (1,3), (1,4), (1,5), (1,6),(2,1), (2,2), (2,3), (2,4), (2,5), (2,6),(3,3), (3,2,), (3,3), (3,4), (3,5), (3,6),(4,1), (4,2), (4,3), (4,4), (4,5), (4,6),(5,5), (5,2,), (5,3), (5,4), (5,5), (5,6),(6,1), (6,2), (6,3), (6,4), (6,5), (6,6) }Total number of events in samplespace = 36Possible outcomes forgetting sum of eight on rolling 2 dice is:{(2,6), (3,5), (4,4), (5,3), (6,2)}Thus, favorable number of outcomes = 5

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