Safety of Children - Assignment Example

Question Null Hypothesis: There is no significant difference in safety between the no. of children. Alternative Hypothesis: There is a significantdifference in safety between the no. of children. Level of significance: 5% level. Descriptives - Safety of Children No. of children n Mean Std. Deviation Std. Error 95% Confidence Interval for Mean Lower Bound Upper Bound One Child 18 3.06 1.35 .32 2.38 3.73 Two Children 18 4.39 1.24 .29 3.77 5.01 Three or More Children 14 5.93 1.07 .29 5.31 6.55 Total 50 4.34 1.67 .24 3.86 4.82 Test of Homogeneity of Variances Safety of Children Levene Statistic df1 df2 Sig. 0.422 2 47 0.658 ANOVA Safety of Children Sum of Squares df Mean Square F Sig. Between Groups 65.069 2 32.535 21.193 .000 Within Groups 72.151 47 1.535 Total 137.220 49 Post Hoc Tests Multiple Comparisons Dependent Variable: Safety of Children LSD Mean Difference (I-J) Std. Error Sig. (I) Number of Children in School (J) Number of Children in School One Child Two Children -1.33(*) .41 .002 Three or More Children -2.87(*) .44 .000 Two Children Three or More Children -1.54(*) .44 .001 Conclusion: From the above ANOVA table, we observe that there is a significant difference in safety between the no. of children. The safety is the highest in three or more children and the lowest in one children case. Question 2: Null Hypothesis: There is no significant difference in overall satisfaction in January between new student groups. There is no significant difference in overall satisfaction in January between titles. There is no significant difference in overall satisfaction in January between new student groups and title groups considered together. Alternative Hypothesis: There is a significant difference in overall satisfaction in January between new student groups. There is a significant difference in overall satisfaction in January between titles. There is a significant difference in overall satisfaction in January between new student groups and title groups considered together. Descriptive Statistics Dependent Variable: Overall Satisfaction in January Type of Student Receives Title 1 Free Lunch Mean SD N New Student No 4.36 1.28 14 Yes 3.62 1.26 13 Total 4.00 1.30 27 Returning Student No 2.50 1.17 12 Yes 3.73 1.19 11 Total 3.09 1.31 23 Total No 3.50 1.53 26 Yes 3.67 1.20 24 Total 3.58 1.37 50 Levenes Test of Equality of Error Variances(a) Dependent Variable: Overall Satisfaction in January F df1 df2 Sig. .092 3 46 .964 Tests the null hypothesis that the error variance of the dependent variable is equal across groups. a Design: Intercept+NEWSTUDE+TITLE1+NEWSTUDE * TITLE1 Tests of Between-Subjects Effects Dependent Variable: Overall Satisfaction in January Source Type III Sum of Squares df Mean Square F Sig. Corrected Model 22.707(a) 3 7.569 5.012 .004 Intercept 625.040 1 625.040 413.856 .000 NEWSTUDE 9.442 1 9.442 6.252 .016 TITLE1 .731 1 .731 .484 .490 NEWSTUDE * TITLE1 12.018 1 12.018 7.958 .007 Error 69.473 46 1.510 Total 733.000 50 Corrected Total 92.180 49 a R Squared = .246 (Adjusted R Squared = .197) Conclusion: From the above ANOVA, we observe that there is a significant difference in overall satisfaction in January between the new student groups as well as between titles. Also there is a significant difference in overall satisfaction in January when new student groups and titles are combined. Question 3: Null Hypothesis: There is no significant difference in overall satisfaction in June between newstudent groups. Alternative Hypothesis: There is a significant difference in overall satisfaction in June between newstudent groups. Level of significance: 5% level. Estimated Marginal Means 1. Type of Student Dependent Variable: Overall Satisfaction in January Mean Std. Error 95% Confidence Interval Type of Student Lower Bound Upper Bound New Student 3.986 .237 3.510 4.463 Returning Student 3.114 .256 2.597 3.630 2. Receives Title 1 Free Lunch Dependent Variable: Overall Satisfaction in January Mean Std. Error 95% Confidence Interval Receives Title 1 Free Lunch Lower Bound Upper Bound No 3.429 .242 2.942 3.915 Yes 3.671 .252 3.165 4.178 3. Type of Student * Receives Title 1 Free Lunch Dependent Variable: Overall Satisfaction in January Mean Std. Error 95% Confidence Interval Type of Student Receives Title 1 Free Lunch Lower Bound Upper Bound New Student No 4.357 .328 3.696 5.018 Yes 3.615 .341 2.929 4.301 Returning Student No 2.500 .355 1.786 3.214 Yes 3.727 .371 2.981 4.473 Descriptive Statistics Dependent Variable: Overall Satisfaction in June Type of Student Mean Std. Deviation N New Student 5.11 .93 27 Returning Student 4.22 .74 23 Total 4.70 .95 50 Levenes Test of Equality of Error Variances(a) Dependent Variable: Overall Satisfaction in June F df1 df2 Sig. 1.729 1 48 .195 Tests the null hypothesis that the error variance of the dependent variable is equal across groups. a Design: Intercept+OSATJAN+NEWSTUDE Tests of Between-Subjects Effects Dependent Variable: Overall Satisfaction in June Source Type III Sum of Squares df Mean Square F Sig. Corrected Model 15.089(a) 2 7.544 12.056 .000 Intercept 82.041 1 82.041 131.105 .000 OSATJAN 5.169 1 5.169 8.260 .006 NEWSTUDE 4.864 1 4.864 7.774 .008 Error 29.411 47 .626 Total 1149.000 50 Corrected Total 44.500 49 a R Squared = .339 (Adjusted R Squared = .311) Conclusion: Therese is a significant difference in overall satisfaction in June between the new student groups since the probability of significance is 0.000. The correlation between satisfaction in January and June is highly significant (p value 0.006). MODULE 6 Question 1: Null Hypothesis: Various correlations are not significant. Alternative Hypothesis: Various correlations are significant. Level of significance: 5% level. Correlations Safety of Children Educational Activities Social Activities Physical Activities Overall Satisfaction in January Overall Satisfaction in June Safety of Children Correlation 1.000 .193 .436(**) .112 .206 .628(**) Prob. . .180 .002 .439 .152 .000 N 50 50 50 50 50 50 Educational Activities Correlation .193 1.000 .317(*) .726(**) .195 .484(**) Prob. .180 . .025 .000 .174 .000 N 50 50 50 50 50 50 Social Activities Correlation .436(**) .317(*) 1.000 .133 .340(*) .555(**) Prob. .002 .025 . .356 .016 .000 N 50 50 50 50 50 50 Physical Activities Correlation .112 .726(**) .133 1.000 .173 .326(*) Prob. .439 .000 .356 . .229 .021 N 50 50 50 50 50 50 Overall Satisfaction in January Correlation .206 .195 .340(*) .173 1.000 .479(**) Prob. .152 .174 .016 .229 . .000 N 50 50 50 50 50 50 Overall Satisfaction in June Correlation .628(**) .484(**) .555(**) .326(*) .479(**) 1.000 Prob. .000 .000 .000 .021 .000 . N 50 50 50 50 50 50 ** Correlation is significant at the 0.01 level (2-tailed). * Correlation is significant at the 0.05 level (2-tailed). The strongest correlation is between educational activities and athletic activities and the weakest correlation is between physical activities and safety of children. Conclusion: The scatterplot shows that there is a good correlation between safety of children and overall satisfaction in June. Conclusion: The scatterplot shows that there is a good correlation between educational activities and overall satisfaction in June. Question 2: Null Hypothesis: The regression coefficient of overall satisfaction on safety of children is not significant. Alternative Hypothesis: The regression coefficient of overall satisfaction on safety of children is significant. Regression Descriptive Statistics Mean Std. Deviation N Overall Satisfaction in June 4.70 .95 50 Safety of Children 4.34 1.67 50 Model Summary Model R R Square Adjusted R Square Std. Error of the Estimate 1 .628(a) .395 .382 .75 a Predictors: (Constant), Safety of Children ANOVA(b) Model Sum of Squares df Mean Square F Sig. 1 Regression 17.569 1 17.569 31.314 .000** Residual 26.931 48 .561 Total 44.500 49 a Predictors: (Constant), Safety of Children b Dependent Variable: Overall Satisfaction in June Coefficients(a) Unstandardized Coefficients Standardized Coefficients t Sig. Model B Std. Error Beta 1 (Constant) 3.147 .297 10.595 .000 Safety of Children .358 .064 .628 5.596 .000 a Dependent Variable: Overall Satisfaction in June Conclusion: The regression coefficient of overall satisfaction on safety of children is highly significant. The overall satisfaction is highly influenced by the safety of children. Null Hypothesis: The multiple regression coefficient of overall satisfaction on safety of children and educational activities is not significant. Alternative Hypothesis: The multiple regression coefficient of overall satisfaction on safety of children and educational activities is significant. Regression Descriptive Statistics Mean SD N Overall Satisfaction in June 4.70 .95 50 Safety of Children 4.34 1.67 50 Educational Activities 5.34 1.15 50 Correlations Overall Satisfaction in June Safety of Children Educational Activities Pearson Correlation 1.000 .628 .484 Sig. (1-tailed) . .000 .000 Conclusion: The multiple regression coefficient of overall satisfaction on safety of children and educational activities is highly significant. Question 3: Null Hypothesis: The stepwise multiple regression of Safety and Education as the independent variables and Overall Satisfaction in June as the dependent variable is not significant.. Alternative Hypothesis: The stepwise multiple regression of Safety and Education as the independent variables and Overall Satisfaction in June as the dependent variable is significant.. Variables Entered/Removed(a) Model Variables Entered Variables Removed Method 1 Safety of Children . Stepwise (Criteria: Probability-of-F-to-enter = .100). 2 Educational Activities . Stepwise (Criteria: Probability-of-F-to-enter = .100). a Dependent Variable: Overall Satisfaction in June Model Summary Model R R Square Adjusted R Square Std. Error of the Estimate 1 .628(a) .395 .382 .75 2 .729(b) .532 .512 .67 a Predictors: (Constant), Safety of Children b Predictors: (Constant), Safety of Children, Educational Activities ANOVA(c) Model Sum of Squares df Mean Square F Sig. 1 Regression 17.569 1 17.569 31.314 .000(a) Residual 26.931 48 .561 Total 44.500 49 2 Regression 23.674 2 11.837 26.713 .000(b) Residual 20.826 47 .443 Total 44.500 49 a Predictors: (Constant), Safety of Children b Predictors: (Constant), Safety of Children, Educational Activities c Dependent Variable: Overall Satisfaction in June Coefficients(a) Unstandardized Coefficients Standardized Coefficients t Sig. Model B Std. Error Beta 1 (Constant) 3.147 .297 10.595 .000 Safety of Children .358 .064 .628 5.596 .000 2 (Constant) 1.662 .479 3.467 .001 Safety of Children .316 .058 .556 5.464 .000 Educational Activities .312 .084 .377 3.712 .001 a Dependent Variable: Overall Satisfaction in June Excluded Variables(b) Beta In T Sig. Partial Correlation Collinearity Statistics Model Tolerance 1 Educational Activities .377(a) 3.712 .001 .476 .963 Conclusion: The safety of children and educational activities has a high influence on overall satisfaction in June. MODULE 7 Application Assignments Question 1: Null Hypothesis: The distribution of no. of children is equal. Alternative Hypothesis: The distribution of no. of children is not equal. Chi Square test for goodness of fit No. of children Observed Expected (O-E) (O-E)2 (O-E)2/E One Child 18 16.67 1.33 1.7689 0.1061 Two Children 18 16.67 1.33 1.7689 0.1061 Three or More Children 14 16.67 -2.67 7.1289 0.4276 Total 50 50 0 0.6399 Conclusion: The chi square value is 0.6399 which is less than 5.99 for 2 d.f., we conclude that the distribution of no. of children is equal. Question 2: Null Hypothesis: The distribution of no. of children is equal. Alternative Hypothesis: The distribution of no. of children is not equal. Chi Square test for goodness of fit Family Size No. of children Observed Expected (O-E) (O-E)2 (O-E)2/E One Child 18 12 6 36 3.00 Two Children 18 26 -8 64 2.46 Three or More Children 14 12 2 4 0.33 Total 50 50 0 5.79 Conclusion: The chi square value is 0.6399 which is less than 5.99 for 2 d.f., we conclude that the distribution of no. of children is equal. Question 3: Null Hypothesis: There family size and title are independent. Alternative Hypothesis: There family size and title are dependent. Family Size * Receives Title 1 Free Lunch Crosstabulation Receives Title 1 Free Lunch Total No Yes Family Size One Child 11 7 18 Two Children 5 13 18 Three or More Children 10 4 14 Total 26 24 50 Chi-Square Tests Value df Asymp. Sig. (2-sided) Pearson Chi-Square 6.947* 2 .031 Likelihood Ratio 7.156 2 .028 Linear-by-Linear Association .145 1 .704 N of Valid Cases 50 a 0 cells (.0%) have expected count less than 5. The minimum expected count is 6.72. Symmetric Measures Value Approx. Sig. Nominal by Nominal Phi .373 .031 Cramers V .373 .031 Conclusion: Since the chi square value is significant at 5% level, we reject the null hypothesis and accept the Alternative Hypothesis and conclude that the family size and title are dependent. Read More