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r tTest for the difference of Means ? ?????????????????????????2121222211 112))1(121 nnnnSnSnSXXS12 = the variance of Group 1 S22 = the variance of Group 2 n1 = the sample size of Group 1 n2 = the sample size of Group 2 Copyright 169。 2022 by Harcourt, Inc. All rights reserved. Degrees of Freedom ? . = n k ? where: –n = n1 + n2 –k = number of groups Copyright 169。 2022 by Harcourt, Inc. All rights reserved. tTest for Difference of Means example ? ?? ? ? ?? ???????????????? ???141211332221 XXS797.? Copyright 169。 2022 by Harcourt, Inc. All rights reserved. 7 97. ??t797.?? Copyright 169。 2022 by Harcourt, Inc. All rights reserved. Type of Measurement Differences between two independent groups Nominal Ztest (two proportions) Copyright 169。 2022 by Harcourt, Inc. All rights reserved. Comparing Two Groups when Comparing Proportions ? Percentage Comparisons ? Sample Proportion P ? Population Proportion ? Copyright 169。 2022 by Harcourt, Inc. All rights reserved. Differences Between Two Groups when Comparing Proportions The hypothesis is: Ho: ?1 ? ?2 may be restated as: Ho: ?1 ? ?2 ? 0 Copyright 169。 2022 by Harcourt, Inc. All rights reserved. A ZTest for Differences of Proportions 21: ?? ?oHor 0:21 ?? ??oH Copyright 169。 2022 by Harcourt, Inc. All rights reserved. ZTest for Differences of Proportions ? ? ? ?212121ppSppZ??????? Copyright 169。 2022 by Harcourt, Inc. All rights reserved. p1 = sample portion of successes in Group 1 p2 = sample portion of successes in Group 2 ??1 ? ?1) = hypothesized population proportion 1 minus hypothesized population proportion 1 minus Sp1p2 = pooled estimate of the standard errors of difference of proportions ZTest for Differences of Proportions Copyright 169。 2022 by Harcourt, Inc. All rights reserved. ZTest for Differences of Proportions to calculate the standard error of the difference of proportions ???????????211121nnqpSpp Copyright 169。 2022 by Harcourt, Inc. All rights reserved. p = pooled estimate of proportion of success in a sample of both groups p = (1 p) or a pooled estimate of proportion