For the t test for independent groups, which of the following describes the weig
ID: 3296026 • Letter: F
Question
For the t test for independent groups, which of the following describes the weighted variance (whose symbol is ____)? The variance across all the data values when both samples are pooled together 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 bar_1 - X bar_2) and the difference in the corresponding population means (mu_1 - mu_2) The difference between the standard deviations of the two samples For the t test for independent groups, which of the following describes the estimated standard error of the difference in sample means (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 bar_1 - X_bar_2) and the difference in the corresponding population means)mu_1 - mu_2) In calculating ____, you typically first need to calculate _______. ______ 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 the difference in sample means 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
for t-test of two independet sample groups the statistic t is given as
t=(mean1-mean2)/((sp*(1/n1 +1/n2)1/2) and sp2=((n1-1)s12+(n2-1)s22)/n and with df is n=n1+n2-2
answer of (first part) right choice is second
::A weighte average of the two sample variaces(weighted by the sample size)
answer of (second part) right choice is third: the difference between the standard deviation of the two samples
(third part)
following information has been generated using the given table
weighted variance= sp2=((n1-1)s12+(n2-1)s22)/n =23.58 and with df is n=n1+n2-2=21+11-2=30
estimated standard error=((sp*(1/n1 +1/n2)1/2) =4.86*sqrt(1/21+1/11)=1.81
t=(27.6-21.5)/1.81=3.37
degrees of freedom for this tobt statistic=21+11-2=30
sample sample size degree of freedom sample mean std deviation sum of square sample1 21 20 27.6 4.5 405 sample2 11 10 21.5 5.5 302.5
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