Sample Sample Sample Sample Consider the data in the table collected from four independent populations. 2 3 4 19 17 10 11 13 18 23 25 a) Calculate the total sum of squares (SST). b) Partition the SST into its two components, the sum of squares between (SSB) and the sum of squares within (SSW). c) Using a = 0.10, what conclusions can be made concerning the population means? Click the icon to view a table of critical F-scores for a = 0.10. Table of Critical F-scores a) Determine the value of SST. SST = (Type an integer or a decimal.) Table of Critical F-scores for a = 0.10. b) Determine the values of SSB and SSW. D SSB = (Type an integer or a decimal.) 2 6 10 D2 60.195 SSW = (Type an integer or a decimal.) 39.863 49.500 53.593 55.83 57.240 8.204 8.906 59.439 59.858 0.367 0.381 9.392 2 8.526 9.00 9.162 9.243 9.293 032 9.349 c) Let H1, H2, H3, and #4 be the population means of samples 1, 2, 3, and 4, respectively. What are the correct hypotheses for a one-way ANOVA test? 5.309 5.28. 5.266 5.252 5.240 5.230 3 5,538 462 5.391 5.343 3.93 3.920 4.545 4.325 4.191 .107 1.051 4.010 3.979 3.955 O B. Ho: Not all the means are equal. 3.780 3.619 5.520 3 453 3.405 3.368 3.316 3.297 4.060 3.339 OA. Ho: My # H2 # H3 # H4 H1 : 41 = H2 = H3 = H4 2.958 2.937 3.776 3.46 3.289 3.18 3.108 3.05 3.014 2.983 H1: 141 = H2 = H3 = H4 2.961 2.883 2.827 78- 2.752 2.725 2.703 3.589 3.257 3.074 OD. Ho: H1 = H2 = H3 = H4 2.924 2.726 2.668 2.589 2.538 3.113 2 806 2.624 2.561 3.458 O C. Ho: H1 = H2 = H3 = H4 H : Not all the means are equal. 9 3.360 3.006 2.813 2695 2.611 2.551 2.505 2.469 2.440 2.416 Hy: H1 # H2 # H3 # H4 10 2.924 2.728 2.605 2.522 2.461 2.414 2.377 2.347 2.323 3.285 11 .860 2.660 2550 2.451 2.389 2342 2.304 2.274 2.248 3.225 2.214 2.188 What is the critical F-score, Fa? 3.177 2.807 2.606 2480 2.394 2.331 2.28 2.245 13 2.347 2.283 2.234 2.195 2.164 2.138 3.13 2.76 2.560 2434 2.095 Fa =(Round to three decimal places as needed.) 14 3.10 2.126 2.522 239. 2.307 2.243 2.19 .154 2.122 3.07. 2.095 2.490 2.361 2.273 2.208 2.158 2.119 2.086 2.059 What is the F-test statistic for this test? 2.028 3.04 2.608 2335 2.244 2.178 2.128 2.088 3.020 2.645 2.437 2308 2.218 2.152 2.102 2.061 2.028 2.001 F= (Round to three decimal places as needed.) 3.007 2.624 2.416 2 286 2.196 2.130 2.079 2.038 2.00. 1.977 1.984 1.956 2.990 2.60 2.397 2.266 2.176 2.109 2.058 2.017 What is the correct conclusion about the population means? 2.97 2.589 2.380 2.249 2.158 2.09 2.040 1909 1.937 all the same 2961 2.57 2.365 2.233 2.142 2.075 2.023 1.982 1.948 1.920 Since the F-statistic is than the critical F-score, the null hypothesis and conclude that the population means 94 2.561 2.219 2.00 067 933 2.351 2.128 1.904 2.937 2.549 2.339 2.207 2.115 2.047 1,992 1.953 1.919 1.890 2027 2.538 .32 2.195 2.103 2.03. 941 1.877 2918 2.52 2.317 2184 2.092 2.024 1.929 .895 1.866 2900 2.519 2.307 2.174 2.082 2.014 196 019 884 1.855 2.901 2.511 2.299 2.165 2.073 2.005 952 1.909 .874 1.845 2.064 .865 1.836 2.894 2 50 2.291 2.157 1043 1900 2.88 2.49 2.283 2.149 2.057 1.988 1.935 1.892 1.857 1.827 2.88 2.48 2.276 2.142 2.049 1.980 1.927 1.884 1.849 1.819
