Please do not answer this using screen shots of your own writing because I canno
ID: 3256275 • Letter: P
Question
Please do not answer this using screen shots of your own writing because I cannot read that! Thanks!
Practice the following problems by hand just to see if you can get the numbers right. Using the following information, calculate the t test statistic. a. X_1 = 62 X_2 = 60 n_1 = 10 n_2 = 10 s^2_1 = 2.45 s^2_2 = 3.16 b. X_1 = 158 X_2 = 157.4 n_1 = 22 n_2 = 26 s^2_1 = 2.06 s^2_2 = 2.59 c. X_1 = 200 X_2 = 198 n_1 = 17 n_2 = 17 s^2_1 = 2.45 s_2^2 = 2.35 Using the results you got from Question 2 and a level of significance at .05, what are the two-tailed critical values associated with each? Would the null hypothesis be rejected?Explanation / Answer
a)
Critical values for two tailed test at 0.05 significance level with df = 18 = +/- 2.101
SE = sqrt[(s1^2/n1) + (s2^2/n2)]
SE = sqrt[(2.45/10) + (3.16/10)]
= 0.7489
t = [ (x1 - x2) - d ] / SE
= [ (62 - 60) - 0 ] / 0.7489
= 2.670
Here, we reject the null hypothesis because 2.670 > 2.101
b)
Critical values for two tailed test at 0.05 significance level with df = 18 = +/- 2.013
SE = sqrt[(s1^2/n1) + (s2^2/n2)]
SE = sqrt[(2.06/22) + (2.59/26)]
= 0.4396
t = [ (x1 - x2) - d ] / SE
= [ (158 - 157.4) - 0 ] / 0.7489
= 1.364
Here, we fail to reject the null hypothesis because 1.364 < 2.013
c)
Critical values for two tailed test at 0.05 significance level with df = 18 = +/- 2.037
SE = sqrt[(s1^2/n1) + (s2^2/n2)]
SE = sqrt[(2.45/17) + (2.35/17)]
= 0.5314
t = [ (x1 - x2) - d ] / SE
= [ (200 - 198) - 0 ] / 0.5314
= 3.7636
Here, we reject the null hypothesis because 3.7636 > 2.037