A new mindfulness program was recently created for adults diagnosed with binge e

Question

A new mindfulness program was recently created for adults diagnosed with binge eating disorder in effort to reduce the amount of binges per week. To determine the significance, the program was recently piloted among 50 adults ages 25-35. The participants were randomly assigned to the control group A or experimental group B and the data is as follows: Control Group A n_1 = 26 x_1 = 7 SS_1 = 70 Experimental Group B n_2 = 24 x_2 = 15 SS_2 = 104 Completing a hypothesis test, determine if the results of this pilot are significant. Include the p value for the calculated result in your interpretation.

Explanation / Answer

1. Null HYpothesis : H0 : xA - bar = xB - bar [ There is no difference betweeen average bings per week for experimental group and the control group]

ALternative Hypothesis Ha: xA - bar < xB - bar [ There is significant difference betweeen average bings per week for experimental group and the control group]

so We will perform a t - test here

First we will collect all the statistics for both groups

Control Group A

Mean xA - bar = 7 , nA = 26 and SS1 = 70 so Variance = SS1 /(nA -1) = 70/25 = 2.8 and std. dev. = 1.6733

For Experiment Group B

Mean xB - bar = 15 , nB = 24 and SS1 = 104 so Variance = SS2 /(nB -1) = 104/23 = 4.52 and std. dev. = 2.1264

pooled std. deviation =sqrt [(nA -1) sa2  + (nB -1)sb2 ] /(nA + nB -2 ) = [ 25 * 1.67332 + 23 * 2.12642]/ 48

= 1.904

test statistic

t = (xA - bar - xB - bar)/ (sp * sqrt(1/nA + 1/ nB) = ( 15 -7) / (1.904 * sqrt(1/26 + 1/24) = 14.84

and for dF = 48, tcritical = 2.011

so t > tcritical so we can say that result is significant here and we can conclude that bings are reduced in control group.

P - value = 0 here for t = 14.84 which is less than significance level alpha = 0.05 .

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