Question

*Calculating the RELATED-samples t-statistic' [15 points Assignment #12 df=7 PROBLEM: A Qwest customer would like to determine if their internet service will actually download files faster if they have the Turbo-Download Boost (TDB) feature turned on. The customer uses the same PC to download the same exact files from the same exact location on the web, first using their internet service with the TDB on, and then with the TDB turned off The data show the number of minutes required to download each file in each condition. There is no population mean difference provided, so just use a value of zero. TDB 'on D TDB 'orr 4 D (difference scores) 3-4 -1 4 2 -4 -2 DO 1- -4 3- 2. 4 - 4 4 - 0 s 2 -5 -3 28 SX-10x = -1.25 the difference between the paired scores in each group = 36 difference score a. Compute the mean and variance for the sample of difference scores. [3] The variance for the D scores is obtained using the formula: S- 15 Sum of squares formula: ss = { x2- x) so = 36 - 5 NOTE: XX for the Related Samples t-statistic is the sum of all the D' values you calculated above 55 = 26-12.5 S of difference scores = 3.3571 2 s? 23.5 35= 36 - Mean of difference scores = -1.25 s 23.5 b. Calculate the estimated standard error for Mo. 13] The estimated standard error for the sample mean formula is: M. F M = 13.3571 = 10.4196 -0. 6478 t-crit=2.365 c. Do the results indicate a significant difference? [3] Use a two-tailed test with a - .05: locate your critical t value you will test against. Calculate the repeated measures t-statistic with the formula: No the results are M, HO -1.25 0 -1.25 -1.9296 pot significant MO 0.6478 - 0.6428 M. -1.25 d. Compute Cohen's d to measure the size of the effect. 131 Cohen's d- -1.25 √5 -0.6822 3.357 1.872 What about the null hypothesis -- what do you conclude-reject or retain Ho? Are the download differences significantly different when using the TDB feature? Explain. 131

Answer 1

n=8 d = 1 Edi a = -1.25 S² = [Edi ²- na 2 n- S2 = 3.3771 Mo = 3.3571 = 8 0.6478 I Ho Hi. "d=0 Mato Hi 14- |-1.25 1 0.6478 1.93 values 2.36 It - Critical I d= -1.25 = -0.6022 3.357 Since 1.93 €2.36, we do not reject Ho and conclude that there is no significant difference in the download when using TDB feature.