Question

In a test of reaction time, we want to know if there is a difference in the speed at which people click on small vs. large buttons. 10 participants are presented with large button sizes and reaction times are measured (in milliseconds). Then 10 different participants, matched in age, are presented with small button sizes, then reaction times are measured. Use an alpha of .05. See below table for summary data:

	Mean	Standard Deviation
Large Buttons	681.60	35.22
Small Buttons	756.80	32.13
Difference	??	28.78

What kind of related-samples t test is this (repeated measures, matched pairs or dependent-samples)? How do you know?

Is this a one-tailed test or a two-tailed test? How do you know?

Answer 1

dependent sample testing;

  The matched-pair t-test (or paired t-test or paired samples t-test or dependent t-test) is used when the data from the two groups can be presented in pairs of befor and after.

repeated measures,

if want two compair two means we use t test,ANOVA compare one or more mean scores with each other; they are tests for the difference in mean scores. The repeated measures ANOVA compares means across one or more variables that are based on repeated observations.

In this case we use two sample,two tailed t test,

if we want to check there is a difference in the two sample, that time we will use two tailed t test,

mu1 != mu2

if we want to check there mu1 is greater then mu2, or mu2 is greater then mu1, that time we use one tailed t test,

mu1 > mu2 or mu2 > mu1

calculation:

1) The provided sample means are : X̅1 = 681.6 X̅2 = 756.8 and the known population standard deviations are : σ1 = 35.22 σ2 = 32.13 and the sample size are n1 = 10.0 and n2 = 10.0. (2) Our test hypothesis is : The following null and alternative hypotheses need to be tested, hypothesis = h0: μ1 = μ2 vs H1: μ1 ≠ μ1 This hypothesis corresponds to a two-tailed, for which a t-test for two population means, with two independent samples, with unknown population standard deviations will be used. (3) Test statistics : The calculation of the z-test proceeds as follows, z = X̅1 - X̅2 681.6 - 756.8 ---------------------- = -------------------------------- = -4.9881 √(σ1²/n1)+(σ2²/n2) √(35.22²/10.0) + (32.13²/10.0) (4) Rejection Criteria : Based on the information provided, the significance level is α = 0.05,and the degrees of freedom are df= 18.0 and the critical value for a two-tailed test is t tabulated = 1.7341 And the rejection region for this two-tailed test is R =[t: |t| > 1.7341] (5) Decision about the null hypothesis : Since it is observed that t calculated means |t| = -4.9881 > t tabulated = 1.7341 it is then concluded that the null hypothesis is Rejected. Using the P-value approach: The p-value is 0.0, and since p =0.0 < α = 0.05 it is then concluded that the null hypothesis is Rejected. (6) Conclusion It is concluded that the null hypothesis Ho is Rejected.. Therefore, there is enough evidence to claim that population mean μ1 is different than μ2 , at the 0.05 significance level.