I am not sure if the answers I have filled in already are correct or not. Differ

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I am not sure if the answers I have filled in already are correct or not.

Differentiating weighted variance and the estimated standard error of the difference in sample means For the t test for independent groups, which of the following describes the estimated standard error of x_1 - x_2 (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 (x_1 - x_2) and the difference in the corresponding population means (mu_1 - mu_2) For the t test for independent groups, which of the following describes the weighted variance (whose symbol is _____)? The difference between the standard deviations of the two samples A weighted average of the two sample variances (weighted by the sample sizes) An estimate of the standard distance between the difference in sample means (x_1 - x_2) and the difference in the corresponding population means (mu_1 - mu_2) The variance across all the data values when both samples are pooled together In calculating the _____ weighted variance _____, you typically first need to calculate the estimated standard error of x_1 - x_2. The estimated standard error of x_1 - x_2 is the value used in the denominator of the t_obt statistic for the t test for independent groups. Suppose you conduct a study using an independent groups research design, and you intend to use the t test for independent groups 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. The weighted variance for your study is _____ The estimated standard error of x_1 - x_2 for your study is _____. The t_obt statistic for your t test for independent groups, when the null hypothesis is that the two population means are the same, is _____. The degrees of freedom for this t_obt statistic is _____.

Explanation / Answer

s = sqrt(SS/df)

SS1 = 6.1^2 * 30 = 1116.3

s2 =sqrt(777.6/15) = 7.2

sp = sqrt((df1* s1^2 + df2 *s2^2 )/(df1 +df2))

=sqrt((1116.3 + 777.6)/45)

=6.48742373109

weighted variance = 6.48742373109^2 = 42.086666

standard error = (sp *sqrt(1/n1 +1/n2))

= 6.4874237 * sqrt(1/31 +1/16)

= 1.99701052502

TS =(X1bar - X2bar)/(sp *sqrt(1/n1 +1/n2))

= (9.8 -9.4)/1.99701052502

= 0.200299

df = df1 +df2 = 45

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