Theory and Problems of Probability and Statistics - Assignment Example

Order # 308106 RELATIONSHIPS BETWEEN THE VARIABLES OF AMOUNTS CLAIMED AND AMOUNTS REIMBURSED IN RELATION TO LEGITIMATE EXPENSE CLIAMS: INFERENTIAL STATISTICS PRESENTATION Ho: Reimbursement is dependent upon claims fulfilling legitimate expense claim criteria The data presented in the previous statistical tables were totally wrong. This is because the researcher failed to cluster the data on sales representative expense accounts into each month and failed to include the seven name representatives. In this connection, the researcher made another computation and formulates new presentations. Data analysis on: Table 1: Comparison of the amounts claimed (X) and amounts reimbursed (Y) in relation to “legitimate” expense claims using analysis of variance (ANOVA) Table 1 show the comparison of the amounts claimed (X) and amounts reimbursed (Y) using analysis of variance (ANOVA). Using 0.05 level of significance, F-statistics, and an Analysis of variance (ANOVA) test, it was established that the df num value is k-1, or 2 -1, or 1 and the df den value is T-k, or 6 - 2, or 4. So, with α = 0.05, the critical value of F in this analysis of variance test was F0.05 (1, 4) = 230. Since computed F (FC) is less than Tabulated F (FT), Ho is accepted. This is because the result of the “Analysis of Variance” (ANOVA) shows that the computed F (12.43) is less than the tabular values of F-statistics (230) at 0.05 degree of freedom (1, 4). This means that there is no significant difference between the variables of amounts claimed and amounts reimbursed in relation to “legitimate” expense claims. Data analysis on: Table 2: Correlation of the amounts claimed (X) and amounts reimbursed (Y) in relation to “legitimate” expense claims using coefficient of determination (R2) Correlation R2 Adjusted R2 Interpretation Amounts claimed (X) and amounts reimbursed (Y) 0.756494365 0.695617957 Very high positive correlation The resultant R Square 0.7565 is very close to 1 and it is above 0.75 which means that the correlation is near normal curve distribution, so, it is interpreted as very high positive correlation. Thus, in percentile (%), 75.65 is an indicator of significant relationship between the variables of amounts claimed and amounts reimbursed in relation to “legitimate” expense claims. Finally, the R square of 0.756494365is quite near to the adjusted R square 0.695617957. This means that the regression model approximately fits the data. Table 3: Other Analysis for the amounts claimed (X) and amounts reimbursed (Y)   Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept 140.868609 26.70413145 5.275161606 0.00619 66.72605391 215.011164 Claimed 0.283748969 0.0804926 3.525155969 0.024337 0.060265684 0.507232254 P-value The variables of amounts claimed and amounts reimbursed in relation to “legitimate” expense claims are not significant in the full regression equation. This is because the p-value of the two variables is not equal to zero. 95% Confidence interval The regression slope of the confidence interval is very short with 0.060265684 to 0.507232254 values which is closer to zero has significant relation to the “legitimate” expense claims. t Stat or test statistics All of the test statistic values were very close to 1.96 which means that the hypothesis is rejected. The test statistics value of the Y-Intercept is z = 140.868609 / 26.70413145 = 5.275161606. The value falls near in the right rejection region. The test statistics value of P Claimed (250.5) = 0.283748969/ 0.0804926= 3.525155969. The value falls near in the right rejection region. Conclusion Reimbursement is dependent upon claims fulfilling legitimate expense claim criteria. References Aczel, Amir D. 1996. Complete Business Statistics. 3rd Ed. USA: Irwin/ McGraw-Hill Companies. Albright, S., Winston, W., & Zappe, C. 2006. Data Analysis and Decision Making with Microsoft Excel. Manson, US: Thomson South-Western, USA. Sander, D. and Smidt, R. 2000. Statistics, A first course. 6th Ed. U.S.A.: McGraw-Hill Higher Education. Spiegel, M., Schiller, J. and Srinivasan, R.A. 2000. Theory and Problems of Probability and Statistics. 2nd ed. U.S.A.: McGraw-Hill. Appendices Microsoft Excels Name Month Category Claimed Reimbursed Adams April Misc $49 $2 Adams April Trip $348 $162 Adams April Entertain $127 $127 Adams April Entertain $212 $151 Adams April Trip $652 $541 Adams April Misc $90 $47 Adams April Entertain $247 $134 $246 $166 Brown April Trip $669 $669 Brown April Misc $83 $83 Brown April Trip $608 $608 Brown April Trip $311 $311 $418 $418 Craig April Trip $720 $21 Jones April Trip $825 $754 Jones April Misc $58 $17 $442 $386 Smith April Entertain $144 $32 Smith April Misc $34 $33 Smith April Misc $54 $25 Smith April Trip $547 $547 Smith April Misc $117 $65 $179 $140 Thompson April Trip $787 $787 Thompson April Entertain $221 $78 Thompson April Misc $49 $25 Thompson April Misc $76 $33 Thompson April Entertain $185 $185 $264 $222 Williams April Misc $29 $14 Williams April Misc $68 $61 Williams April Trip $758 $758 Williams April Trip $811 $811 Williams April Trip $423 $42   Average   $418 $337 Summary of the data   Claimed April June March May Average Claimed 1 Adams $246 $344 $303 $109 $251 2 Brown $418 $374 $157 $208 $289 3 Craig $720 $464 $605 $252 $510 4 Jones $442 $449 $290 $198 $345 5 Smith $179 $224 $77 $411 $223 6 Thompson $264 $109 $631 $209 $303 7 Williams $418 $0 $323 $205 $237   Reimbursed April June March May Average Reimbursed 1 Adams $166 $327 $211 $93 $199 2 Brown $418 $344 $127 $99 $247 3 Craig $21 $464 $358 $252 $274 4 Jones $386 $442 $72 $104 $251 5 Smith $140 $213 $70 $335 $190 6 Thompson $222 $106 $479 $128 $234 7 Williams $337 $0 $261 $167 $191   Claimed Average Claimed Average Reimbursed 1 Adams $251 $199 2 Brown $289 $247 3 Craig $510 $274 4 Jones $345 $251 5 Smith $223 $190 6 Thompson $303 $234 7 Williams $237 $191 Computation results from Microsoft Excel Program SUMMARY OUTPUT Regression Statistics Multiple R 0.869766845 R Square 0.756494365 Adjusted R Square 0.695617957 Standard Error 18.77985715 Observations 6 ANOVA   df SS MS F Significance F Regression 1 4382.694945 4382.694945 12.42672 0.024336591 Residual 4 1410.732139 352.6830346 Total 5 5793.427083         Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept 140.868609 26.70413145 5.275161606 0.00619 66.72605391 215.011164 250.5 0.283748969 0.0804926 3.525155969 0.024337 0.060265684 0.507232254 RESIDUAL OUTPUT Observation Predicted 199.25 Residuals Standard Residuals 1 222.9429982 24.05700182 1.432201826 2 285.6515203 -11.90152029 -0.708541289 3 238.691066 12.30893405 0.732796129 4 204.0736918 -14.57369176 -0.867625488 5 226.9154837 6.834516255 0.406883897 6 207.9752401 -16.72524008 -0.995715075 PROBABILITY OUTPUT Percentile 199.25 8.333333333 189.5 25 191.25 41.66666667 233.75 58.33333333 247 75 251 91.66666667 273.75 Read More