Chapter 10, question 5: please answer all

Complete. 5. Differentiating pooled variance and the estimated standard error of the difference in sample means For the independent-measures t test, which of the following describes the estimated standard error of M, - M, (whose symbol is )? A weighted average of the two sample variances (weighted by the sample sizes) The variance across all the data values when both samples are pooled together The difference between the standard deviations of the two samples An estimate of the standard distance between the difference in sample means (M, - M,) and the difference in the corresponding population means (H, - H2) For the independent-measures t test, which of the following describes the pooled variance (whose symbol is )? A weighted average of the two sample variances (weighted by the sample sizes) The variance across all the data values when both samples are pooled together An estimate of the standard distance between the difference in sample means (M, - M2) and the difference in the corresponding population means (H, - H2) The difference between the standard deviations of the two samples In calculating the , you typically first need to calculate the . The is the value used in the denominator of the t statistic for the independent-measures t test. Suppose you conduct a study using an independent-measures research design, and you intend to use the independent-measures t test to test whether the means of the two independent populations are the same. The following is a table of the information you gather. Fill in any missing values. Sample Degrees of Sample Standard Size Freedom Mean Deviation Sums of Squares Sample n, = 21 M, = 27.6 S, = 4.5 1 Sample n, = 11 M, = 21.5 SS, = 302.5 2 The pooled variance for your study is . (Note: You are being asked for this value to three decimal places, because you will need to use it in succeeding calculations. For the most accurate results, retain these three decimal places throughout the calculations.) The estimated standard error of M, - M, for your study is The t statistic for your independent-measures t test, when the null hypothesis is that the two population means are the same, is Y The degrees of freedom for this t statistic is