Slide 1Slide 2Slide 3Slide 4Slide 5Slide 6Slide 7Slide 8Slide 9Slide 10Slide 11Slide 12Slide 13Slide 14Slide 15Slide 16Slide 17Slide 18Slide 19Slide 20Slide 21Slide 22Slide 23Slide 24Slide 25Slide 26Slide 27Slide 28Slide 29Slide 30Slide 31Slide 32Slide 33Slide 34Slide 35Slide 36Slide 37Slide 38Slide 39Slide 40Slide 41Slide 42Slide 4301/14/19 Slide 1SOLVING THE PROBLEMThe one sample t-test compares two values for the population mean of a single variable. The two-sample test of a population means compares the population means for two groups of subjects on a single variable. The null hypothesis for this test is:there is no difference between the population mean of the variable for one group of subjects and the population mean of the same variable for a second group of subjects.In addition to our concern with the assumption of normality for each group and the number of cases in each group if we are to apply the Central Limit Theorem, but this test also requires us to examine the spread or dispersion of both groups so that the measure of standard error used in the t-test fairly represents both group.While there is a test of Equality of Variance and a formula to use when the test is satisfied and a formula to use when the test is violated, the authors of our text suggest we always use the formula that assumes the test is violated. If we use this version of the statistic when the variances are in fact equal, the results of the test are comparable to what we would obtain using the formula for equal variances.We will the authors advice and restrict our attention to the “Equal variances not assumed” row in the SPSS output table without examining the Levene test of equality of variance.01/14/19 Slide 2The introductory statement in the question indicates:•The data set to use (GSS2000R)•The variables to use in the analysis: socioeconomic index [sei] for groups of survey respondents defined by the variable sex [sex]•The task to accomplish (two-sample t-test for the difference between sample means)•The level of significance (0.05, two-tailed)01/14/19 Slide 3The first statement asks about the level of measurement.A two-sample t-test for the difference between sample means requires a quantitative dependent variable and a dichotomous independent variable.01/14/19 Slide 4"Socioeconomic index" [sei] is quantitative, satisfying the level of measurement requirement for the dependent variable. "Sex" [sex] is dichotomous, satisfying the level of measurement requirement for the independent variable. Mark the statement as correct.01/14/19 Slide 5A two-sample t-test for the difference between sample means requires that the distribution of the variable satisfy the nearly normal condition for both groups. We will operationally define the nearly normal condition as having skewness and kurtosis between -1.0 and +1.0 for both groups, and not having any outliers with standard scores equal to or smaller than -3.0 or equal to or larger than +3.0 in the distribution of scores for either group.To justify the use of probabilities based on a normal sampling distribution in testing hypotheses, either the distribution of the variable must satisfy the nearly normal condition or the size of the sample must be sufficiently large to generate a normal sampling distribution under the Central Limit Theorem.01/14/19 Slide 6To evaluate the variables conformity to the nearly normal condition, we will use descriptive statistics and standard scores.We will first compute the standard scores.To compute the standard scores, select the Descriptive Statistics > Descriptives command from the Analyze menu.01/14/19 Slide 7First, move the variable for the analysis sei to the Variable(s) list box.Third, click on the OK button to produce the output.Second, mark the check box Save standardized values as variables.01/14/19 Slide 8There were no outliers that had a standard score less than or equal to -3.0.Sort the column Zsei in ascending order to show any negative outliers at the top of the column.01/14/19 Slide 9There were no outliers that had a standard score greater than or equal to +3.0.Sort the column Zsei in descending order to show any positive outliers at the top of the column.01/14/19 Slide 10Next, we will use the Explore procedure to generate descriptive statistics for each gender..To compute the descriptive statistics, select the Descriptive Statistics > Explore command from the Analyze menu.01/14/19 Slide 11First, move the dependent variable sei to the Dependent List.Second, move the group variable sex to the Factor List.Third, mark the option button to display Statistics only.Fourth, click on the OK button to produce the output.01/14/19 Slide 12For survey respondents who were male, "socioeconomic index" satisfied the criteria for a normal distribution. The skewness of the distribution (0.539) was between -1.0 and +1.0 and the kurtosis of the distribution (-0.852) was between -1.0 and +1.0.01/14/19 Slide 13For survey respondents who were female, "socioeconomic index" satisfied the criteria for a normal distribution. The skewness of the distribution (0.610) was between -1.0 and +1.0 and the kurtosis of the distribution (-0.921) was between -1.0 and +1.0.01/14/19 Slide 14For survey respondents who were male, "socioeconomic index" satisfied the criteria for a normal distribution. The skewness of the distribution (0.539) was between -1.0 and +1.0 and the kurtosis of the distribution (-0.852) was between -1.0 and +1.0. For survey respondents who were female, "socioeconomic index" satisfied the criteria for a normal distribution. The skewness of the distribution (0.610) was between -1.0 and +1.0 and the kurtosis of the distribution (-0.921) was between -1.0 and +1.0.There were no outliers that had a standard score less than or equal to -3.0 or greater than or equal to +3.0.Mark the statement as correct.01/14/19 Slide 15To apply the Central Limit Theorem for a two-sample t-test for the difference between sample means requires that both groups defined by the independent variable have 40 or more cases.Though we have satisfied the nearly normal condition and do not need to utilize the Central Limit Theorem to justify the use of probabilities based on the normal distribution, we will still examine the sample size.01/14/19 Slide 16There were 110 valid cases for survey respondents who were male and 145 valid cases for survey respondents who were female.01/14/19 Slide 17Both groups had 40 or more cases, so the Central Limit