Question

Use SPSS and work the difference of two means problem Your task is to determine if Weight Lifters of Group B have more weight gain than Weight Lifters of Group A. Translate your computer readout into the 6 step hypothesis testing model. Test the assumption at 5% error. Remember, is this a one-tailed or two-tailed alternative hypotheses? What type of test does SPSS conduct (one or two- tailed)? Pay attention to your critical value. Weight Gain Weight Lifters - Group A Weight Lifters - Group B 2.4

Answer 1

1) Null hypothesis:

H0: Mean of weight lifter GROUP A = GROUP B

2) Alternative Hypothesis:

H1: Mean of Weight of GROUP B> GROUP A

Here we conduct the one-tailed test because it depends on the alternative hypothesis our alternative hypothesis is one-sided GROUP B>GROUP A.

SPSS output

— Т-Test [DataSet0 Group Statistics Std. Error Mean Std. Deviation Mean group 3335 weight 10 2.170 1055 group a 10 2.460 4402 1392 group b Independent Samples Test Levene's Test for Equality of Variances t-test for Equality of Means 95% Confidence Interval of the Difference Std. Error Mean F Sig. df Sig. (2-tailed) Difference Difference Lower Upper Equal variances 1.661 -2900 weight .907 .354 18 .114 .1746 .6569 0769 assumed Equal variances not -.6588 -1.661 16.771 115 2900 1746 0788 assumed

3)Calculation of the critical value

here we have two independent samples n1 & n2 so for two sample degree of freedom is n1+n2-2=10+10-2=18

so for using t table for 0.05 significance level critical value is 1.734

4)Calculation of test statistic

s²_p = ((df₁/(df₁ + df₂)) * s²₁) + ((df₂/(df₂ + df₂)) * s²₂) = ((9/18) * 0.11) + ((9/18) * 0.19) = 0.15

s²_M1 = s²_p/N₁ = 0.15/10 = 0.02
s²_M2 = s²_p/N₂ = 0.15/10 = 0.02

t = (M₁ - M₂)/√(s²_M1 + s²_M2) = -0.29/√0.03 = -1.66

also, spss gives test statistic value t=-1.66

5)Statistical decision:

Here p-value 0.354>0.05 so we accept null hypothesis so there is no statistical difference between this group

6)statistical decision

weight lifter of group A and weight lifter of group B are the same