Analysis of Socioeconomic and Demographic Variables: Descriptive, Hypothesis Testing, and Chi-Square Tests

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Analysis of Socioeconomic and Demographic Variables: A StatisticalApproach Using Descriptive, Hypothesis Testing, and Chi-Square TestsBased on the dataset provided, you are required to analyzeand interpret the relationship betweenvarious continuous and discrete variables. You are expected to focus on the following:1.Descriptive Statistics for Continuous Variables:oWealth ScoreoMedian School YearsoAgeFor each continuous variable, calculate and interpret the following measures:•Mean•Median•Mode•Variance•Standard DeviationProvide a detailed explanation of the observed patterns and suggest what the distribution of eachvariable might look like based on the statistical measures (e.g., bimodal, normal, skewed).2.Analysis of Discrete Variables:

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oMarital StatusoPresence of ChildrenoGenderProvide frequency tables and bar graphs for each of the discrete variables, and interpret thefindings. Specifically, discuss the relationship between thecategories within each variable andprovide insights based on the count distribution.3.T-test Analysis:Perform t-tests to determine if there is a significant difference betweenthe means of the following pairs:oWealth Score of Married vs. SingleoMedian School Years of Married vs. SingleoAge of Married vs. SingleoWealth Score of Males vs. FemalesoMedian School Years of Males vs. FemalesoAge of Males vs. FemalesFor each t-test, state the null and alternative hypotheses, provide the test results, andinterpret thefindings. Be sure to include the p-value and explain whether the null hypothesis is rejected ornot.4.Chi-SquareTest:PerformChi-Squareteststoexaminetheindependenceofthefollowing pairs:

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oMarital Status and Wealth ScoreoMarital Status and Median School YearsoMarital Status and AgeoGender and Wealth ScoreoGender and Median School YearsoGender and AgeFor each Chi-Square test, state the null and alternative hypotheses, provide the test results, andinterpret the findings. Discuss whether the null hypothesis is rejected or not based on the p-value.5.Handling Missing Data:Discuss the potential impact of missing data on the accuracy ofthe statistical results. How can missing data influence parameter estimates and overallfindings? Suggest methods to handle missing data in future analyses.Word Count Requirement:•Total word count:800-1000 words

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Three continuous variables chosen are Wealth Score, Median School Years and Age. whereas,three discrete chosen variables are Marital Status, Presence of Children and gender.Continuous variablesWealth ScoreVariablemeanmedianmodevariancestandard deviationWealth Score301.8376299.01490.468902.2956494.35197741Here, it is observed thatmean isapproximately equal to median. And mode is greaterthan mean and median. This gives me an idea that graph of Wealth score must beBimodal. Meanis sum of all observations divided by total number of observations. Here, mean is 301.8376implying that an averageWealth Scoreis 301.8376.The median in an ascending series is thevalue at which there are just as many values less than it as there are greater than it. Here medianis 299.01 which is approximately equal to mean. Thus I can say that, half of the wealth score ismore than 299.01 and that of other half is less than 299.01. Mode is the number which occurmaximum number of times. Here mode is 490.46 implying wealth score of maximum number ofpeopleis490.46.The variance and the standard deviation are both measures of thespreadof thedistribution about the mean. The standard deviation measures how concentrated the data arearound the mean; the more concentrated, the smaller the standard deviation. Standard deviationmeasures spread in the same physical unit as the original data. Standard deviation and variance isgiven in the table above. Thehighvalue of standard deviation implies that my mean isnot muchreliable.

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The frequency table for Wealth score is shown below:BinFrequency1009200290300714400667500320More0And the corresponding histogram is shown belowIt is observed that shape of the distribution of wealth score is Bimodal. That is it has 2 modes.The same is observed from numeric data.0200400600800100200300400500MoreFrequencyBinHistogramFrequency

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Median School YearsVariablemeanmedianmodevariancestandard deviationMedian School Years13.2632213.2122.030528451.424966124Here, it is observed that mean is approximately equal to median and also to mode. This gives mean idea that graph ofMedian School Yearsmust be Normal. Mean is sum of all observationsdivided by total number of observations. Here, mean is 13.2 implying that an averageMedianSchool Yearsis 301.8376.The median in an ascending series is the value at which there are justas many values less than it as there are greater than it. Here median is 13.2 which isapproximately equal to mean. Thus I can say that, half of theMedian School Yearsis more than299.01 and that of other half is less than 13.2. Mode is the number which occur maximumnumber of times. Here mode is 12 implyingMedian School Yearsof maximum number ofpeople is 12.The variance and the standard deviation are both measures of thespreadof thedistribution about the mean. The standard deviation measures how concentrated the data arearound the mean; the more concentrated, the smaller the standard deviation. Standard deviationmeasures spread in the same physical unit as the original data. Standard deviation and variance isgiven in the table above. The low value of standard deviation implies that my mean is reliable.

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The frequency table forMedian School Yearsis shown below:BinFrequency507.5110112.56951594917.8256201More0And the corresponding histogram is shown belowIt is observed that distribution ofMedian School Years isapproximately normal.and the same isobserved from numeric data.05001000FrequencyBinHistogramFrequency

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