Question

For the independent measures ttast, which of the following describes the estimated standard error of the difference in sample means (whose symbolis )? The difference between the standard deviations of the two samples A weighted average of the two sample variances (weighted by the sample stres) An estimate of the standard distance between the difference in sample means (M. - Me) and the difference in the corresponding population means (Hi-Pa) The variance across all the data values when both samples are pooled together For the independent measures ttest, which of the following describes the pooled variance (whose symbol is O O O O The difference between the standard deviations of the two samples 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 (Mi-M) and the difference in the corresponding population means ( a) is the value used in In calculating you typically first need to calculate 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 ttest 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 Sire Degrees of Freedom Sum of Squares Standard Deviation - 54 Sample Mean M-45 M -16 Sample 1 Sample 2 b The police arance for your study is (Note: You are asked for this value to three decal e you wild to succeeding calculations. For the most access the theme throughout the calculations)

Answer 1

SE

Third option is correct.

$s^{2}_{p}$

Fourth option is correct.

In calculating the t test statistics, you first need to calculate the standard error. The standard error is the value used in the denominator of the t test statistics ....

Sample 1 :

dfi = n1 -1 = 11 -1 = 10

SS1 = s(n1 - 1) = 5.42 . 10 = 291.6

Sample 2:

df2 = n2-1 = 21 -1 = 20

S2 = 1/ SS2 V no-1 V 1248.2 20 = 7.9

The pooled variance is

2 _ (n1 – 1)sť + (n2 – 1) s} – 51.3267 ni+n2 - 2

The standard error is

$11-12 = Sp1 —+-= 2.6665 V ni n2

The test statistics is:

T1 - T2 t 4.5 – 3.6. - = 0.338 SpV1+1 2.6665 +

Here degree of freedom will be

df = n1 + n2 - 2 = 11 +21 – 2 = 30