Consider a research situation involving two independent samples, Sample A and Sa

Question

Consider a research situation involving two independent samples, Sample A and Sample B. (Assume you’re subtracting the mean of Sample B from the mean of Sample A). Mean of Sample A = 4.5 (n=15); Mean of Sample B = 6.5 (n=13); Estimate of the standard error of the difference of means (s x1- x2) = 1.5. Calculate the t statistic, identify the degrees of freedom, identify the critical value (assume a .05 level of significance), and state whether you would accept or reject the null hypothesis. Write your findings (i.e., t statistic, degrees of freedom, critical value, and acceptance or rejection of the null) below Consider a research situation involving two independent samples, Sample A and Sample B. (Assume you’re subtracting the mean of Sample B from the mean of Sample A). Mean of Sample A = 4.5 (n=15); Mean of Sample B = 6.5 (n=13); Estimate of the standard error of the difference of means (s x1- x2) = 1.5. Calculate the t statistic, identify the degrees of freedom, identify the critical value (assume a .05 level of significance), and state whether you would accept or reject the null hypothesis. Write your findings (i.e., t statistic, degrees of freedom, critical value, and acceptance or rejection of the null) below

Explanation / Answer

A:

x1 = 4.5

n1 = 15

B:

x2 = 6.5

n2 = 13

SE = sqrt[ (s1^2/n1) + (s2^2/n2) ] = 1.5

Let

Null hypothesis: 1 - 2 = 0

Alternative hypothesis: 1 - 2 0

t- statistic=  [ (x2 - x1) - d ] / SE = [(6.5-4.5)-0]/1.5 = 1.33

df = n1+n2-2 = 15+13-2 = 26

At 0.05 LoS, t-critical = 1.706

t-stat < t-critical

Cannot reject H0

Hope this helps :)

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