Attachment # 00011813 - MBA_5652-18O-7_Research_Methods_Unit_IV_Scholarly_Activity.docx
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Unit IV Scholarly ActivityMBA 5652-18O-7, Research MethodsPatrese Williams 191570Columbia Southern UniversityThe correlation: Test for AssociationThe hypothesis for this test is:Ho: Employee annual sick days and particular matter do not associate significantlyH1: Employee annual sick days and particular matter associates significantly micronsmean annual sick days per employeemicrons1mean annual sick days per employee-0.715981The correlation Coefficient.The correlation coefficient at 95% level of significance is -0.71598. This implies a strong negative association. We therefore reject the null hypothesis and conclude that employee annual sick days and particular matter associates significantly.Assumptions.The level of measurement for both the data sets is scale. There are no outliers in the data (Andrew, et al, 2013).The data follows a normal distribution as indicated by the close to equal measures of central tendency. left381000Microns12345678910111213Frequency877101391518106000Mean annual sick days per employee12345678910111213Frequency011513182418127220Frequency distributions and histogram representation for both variablesmicrons mean annual sick days per employee Mean5.657281553Mean7.126213592Standard Error0.255600143Standard Error0.186483898Median6Median7Mode8Mode7Standard Deviation2.59405814Standard Deviation1.892604864Sample Variance6.729137636Sample Variance3.58195317Kurtosis-0.8521619Kurtosis0.124922603Skewness-0.37325713Skewness0.142249784Range9.8Range10Minimum0.2Minimum2Maximum10Maximum12Sum582.7Sum734Count103Count103Confidence Level (95.0%)0.506981673Confidence Level (95.0%)0.369889928Descriptive statistics for both variables.Measures of Central Tendency and Scale of MeasureThe mean, mode and median for microns is 5.657, 8, and 6. This implies a slight variation from equality and thus the data have a slight skewness but close to normal. The measures of central tendency for sick days are 7.126, 7, and 7, implying a perfect normal distribution. The scale of measure for the data is ratio.Simple Regression: Model Effectiveness in PredictionHo: The slope of the model is equal to zeroHa: The slope of the equation is significantly different from zero The multiple r =0.94, while r2 = 0.88, at α = 0.05, significant F value is 7.66E-105 < 0.05, this indicates that the safety training accounts for 88% of the lost time. The 95% confidence interval for the intercept is (268.196, 278.70) indicating that zero is not include.The model for prediction is; yi = 273.45 – 0.14XiWe therefore reject the null hypothesis and conclude that the slope of the equation is significantly different from zero The assumptions for this test is that the all the data are pared and the dependent variable is normally distributed ((Yoo, & Harman, 2012). 069278500Frequency distributions and Histogram representation of the variables. training expenditure lost time hours Mean595.9843812Mean188.0044843Standard Error31.4770075Standard Error4.803089447Median507.772Median190Mode234Mode190Standard Deviation470.0519613Standard Deviation71.72542099Sample Variance220948.8463Sample Variance5144.536016Kurtosis0.444080195Kurtosis-0.501223533Skewness0.951331922Skewness-0.081984874Range2251.404Range350Minimum20.456Minimum10Maximum2271.86Maximum360Sum132904.517Sum41925Count223Count223Confidence Level (95.0%)62.03197147Confidence Level (95.0%)9.465483893Measures of Central Tendency and scale of measure The mean mode and median for the training expenditure is 595.98, 234, and 507.77. The data indicates skewness to the right. The mean, mode and median are 188, 190 and 190, implying a negligibly skewed. The data is normally distributed. The histogram representations of the data also show the shapes. The scale of measure for this data is ratioMultiple Regression to Determine level of Noise in the WorkplaceLevel of noise in decibel is the dependent variable.H0: The slope of the model is not significantly different from zeroHa: The slope of the model is significantly different from zero. Multiple Regression excel output The multiple r = 0.6, while r2 = 0.36, therefore the independent variables accounts for 36% of the dependent variable, level of noise. The significance F for the intercept is 2.1E-143 < 0.05, while the p-values for the other variables are, Frequency is 4.1E-104<0.05, Angle is 0.204˃0.05, Chord length is 0.06˃0.05, velocity is, 1.02E-18<0.05, while that for displacement is 5.21E-45<0.05 The 95% confidence interval for two variables, chord length and angle include zeroModel of predicting level of noise is yi = 126.82 – 0.0011x1 + 0.0473x2 – 5.495x3+ 0.083x4 – 240.506x5 Since two of the variables have p-value greater than the critical value and the confidence intervals of the two variables includes zero, we therefore fail to reject the null hypothesis and conclude the slope of the model is not significantly different from zeroAssumptions (Yoo, & Harman, 2012).Data should not be related to the residuals, this assumption is not met There is no linearity between the dependent and the independent variablesThe population from which the data was draw do not follow normal distributions.Frequency distribution for Frequency & Angle variablesFrequency distribution for Noise level & Displacement variablesFrequency distribution table for Velocity variable & Chord length Variableleft26035000Histograms representing Angle & Frequency variables 0285750Histograms representing Velocity & Chord Length variableslefttopHistograms representing Noise level & displacement variablesDescriptive statistics for the variablesMeasures of central tendency and scale of measure The only data with measures of central tendency implying a normal distribution is the level of noise in decibel. This is indicated by 124.8, 127.3 and 125.7, mean mode and median respectively. The rest of the variables have skewed distributions indicated by large variations in the measures of central tendency. The scale of measure for all the data variables in the test is ratioT-test for independent samplesH0: The means for the populations from which the data was drawn are not significantly differentH1: The means for the populations from which the data was drawn are significantly differentt-Test: Two-Sample Assuming Unequal Variances Group A Prior Training ScoresGroup B Revised Training ScoresMean69.7903225884.77419355Variance122.00449526.96456901Observations6262Hypothesized Mean Difference0Df87t Stat-9.666557191P(T<=t) one-tail9.69914E-16t Critical one-tail1.662557349P(T<=t) two-tail1.93983E-15t Critical two-tail1.987608282 T-test for difference in mean The sample means X-bar for the two variables are 69.79032 and 84.7742. P-value is 1.93983E-15, 1.93983E-15 < 0.05 therefore we reject the null hypothesis and conclude that the means for the populations from which the data was drawn are significantly different.Assumptions The data scale of measurement is ratioThe technique of drawing the sample was randomized.The measures of central tendency were drawn from populations following normal distribution as indicated by the plots and the measures of central tendency (Garson, 2012).. Group A Prior Training Scores50556065707580859095Frequency4531191011351Group B Revised Training Scores74767880828486889092949698Frequency04376911774121Frequency Distributions tablesleft34607500Histogram representationsGroup A Prior Training Scores Group B Revised Training Scores Mean69.79032258Mean84.77419355Standard Error1.402788093Standard Error0.659478888Median70Median85Mode80Mode85Standard Deviation11.04556449Standard Deviation5.192741955Sample Variance122.004495Sample Variance26.96456901Kurtosis-0.77667598Kurtosis-0.352537913Skewness-0.086798138Skewness0.144084526Range41Range22Minimum50Minimum75Maximum91Maximum97Sum4327Sum5256Count62Count62Confidence Level (95.0%)2.805048156Confidence Level (95.0%)1.318709538Descriptive statistics tableMeasures of central Tendency and scale of measure Group B measures of central tendency indicates a perfect normal distribution since the variation is very slight. While on the other hand, that for group A training follows a slightly skewed distribution because the variation from the mean is higher.The scale of measurement for these data is ratio because it represents results in figures.Paired Samples T-test H0: The average blood lead level for the group before exposure and after exposure to lead are not significantly differentH1: The average blood lead level for the group before exposure and after exposure to lead are significantly differentt-Test: Paired Two Sample for Means Pre-Exposure μg/dLPost-Exposure μg/dLMean32.8571428633.28571429Variance150.4583333155.5Observations4949Pearson Correlation0.992236043Hypothesized Mean Difference0df48t Stat-1.929802563P(T<=t) one-tail0.029776357t Critical one-tail1.677224196P(T<=t) two-tail0.059552714t Critical two-tail2.010634758 T-test for to paired samples. At 95% level of significance, the critical value is -1.92980, while the p-value for the one tailed test is 0.029776. Thus, 0.029776< 0.05 and therefore we reject the null hypothesis and conclude that the average blood lead level for the group before exposure and after exposure to lead are significantly differentAssumptions:The data are independent (Garson, 2012).The populations from which the data was drawn follows a normal distribution. The scale of measure for both variables is ratio/intervalPre-Exposure μg/dL4812162024283236404448525660Frequency022234349484310Post-Exposure μg/dL4812162024283236404448525660Frequency0222343456104310Frequency distribution tablesleft29146500 Histogram representationsPre-Exposure μg/dLPost-Exposure μg/dLMean32.8571429Mean33.28571429Standard Error1.75230655Standard Error1.781423416Median35Median36Mode36Mode38Standard Deviation12.2661458Standard Deviation12.46996391Sample Variance150.458333Sample Variance155.5Kurtosis-0.5760371Kurtosis-0.654212507Skewness-0.4251097Skewness-0.483629097Range50Range50Minimum6Minimum6Maximum56Maximum56Sum1610Sum1631Count49Count49Confidence Level (95%)3.52324845Confidence Level (95%)3.581791839Descriptive statistics tableMeasures of Central tendency and scale of measurement Both data indicate a slight skewness to the left as indicated by the smaller means as compared to both medians and modes. The data is thus approximately normally distributed. The shapes of the histogram plots are both bell-shaped, confirming the distribution. The scale of measurement for the data is intervalANOVA One-Way test H0: µA = µB = µC = µDH1: µA ≠ µB≠ µC≠ µDANOVA: Single FactorSUMMARYGroupsCountSumAverageVarianceA = Air201788.99.357895B = Soil201829.13.042105C = Water2014076.631579D = Training201085.41.410526ANOVASource of VariationSSdfMSFP-valueF critBetween Groups182.8360.9333333311.92311.76E-06 2.724944Within Groups388.4765.110526316Total571.279 One-ANOVA test table The sample means X-bar for A, B, C, D are 8.9, 9.1, 7 and 5.4. The significance value is α = 0.05. The critical value, F = 2.7249, while the P-value is 1.76E-06< 2.7249. We fail to reject null hypothesis and the mean returns on investment for A, B, C, and D are not significantly different.AssumptionsThe scale of measure for the data is interval (Cardinal, & Aitken, 2013)The population from which the data was drawn follows normal distribution.A = Air234567891011121314Frequency0112103323211B = Soil234567891011121314Frequency0000125532110C = Water234567891011121314Frequency0114531111200D = Training234567891011121314Frequency0137621000000left3530600Frequency distribution tablesHistogram representationsleft34925000Histogram representationsThe descriptive statistics tableMeasures of central tendency and measures of scale The measures of central tendency for the training, water, and soil are slightly skewed to the right but approximately follow normal populations. This is indicated by slightly greater mean than the mode and median. The air variable has a skewness to the left as the mean is less than the median and the mode. The scale of measure for all the data sets is intervalReferencesAndrew, G., Arora, R., Bilmes, J., & Livescu, K. (2013, February). Deep canonical correlation analysis. In International conference on machine learning (pp. 1247-1255).Cardinal, R. N., & Aitken, M. R. (2013). ANOVA for the behavioral sciences researcher. Psychology Press.Creswell, J. W., & Creswell, J. D. (2017). Research design: Qualitative, quantitative, and mixed methods approaches. Sage publications.Garson, G. D. (2012). Testing statistical assumptions. Asheboro, NC: Statistical Associates Publishing.Yoo, S., & Harman, M. (2012). Regression testing minimization, selection and prioritization: a survey. Software Testing, Verification and Reliability, 22(2), 67-120.
Solution: resarch paper assignment