4. Differentiating pooled variance and the estimated standard error of the difference in sample means For the independ entmeasures t test, which of the following describes the estimated sta ndancl error of the difference in sample means {whose symbol is V 'j? C) The difference between the standard deviations of the two samples 0 A weighted avenge of the two sample variances (weighted by the sample sizes) 0 An estimate of the standard distance between the difference in sample means (M1 H2) and the difference in the corresponding population means [[11 pa} 0 The variance across all the data values when bo1 samples are pooled toge'ler For the independentmeasures t testr which ofthe following describes the pooled variance {whose symbol is V 3'? Q A weighted avenge of the two sample variances (weighted by the sample sizes) 0 The difference between the standard deviations of the two samples C? An estimate of the standard distance between the difference in sample means (M1 H2) and the difference in the corresponding population means ([11 pa) 0 The variance across all the data values when bo1 samples are pooled toge'ler In calculating V ,. you typicallyr rst need to calculate V . V is the value used in the denominator of the t statistic for the independ entmeasures t test. Suppose you conduct a study using an independentmeasures research design, and you intend to use the independentmeasures: t testto test whether the means of the two independent populaons are the same. The following is a table of the information you gather. Fill in any missing values. Sample Size Degrees of Freedom Sample Mean Standard Deviation Sums of Squares Sample 1 n1 = 31 7 M1 = 9.3 s: = 5.1 7 Sample 2 n: = 16 7 M2 = 9.4 V 552 = 3"?16 The pooled variance for your study is V . (Note: You are being asked for iis value to three decimal places, because you will need to use it in succeeding calculaons. For the most accurate results, retain these three decimal places throughout the calculations.) The estimated standard error of the difference in sample means for your study is V . The t stalistic for your independent-measures t test, when the null hypothesis is that the two population means are the sa me. is V . The degrees of freedom for this t statistic is V