A social worker is interested in examining how people who have higher levels of

Question

A social worker is interested in examining how people who have higher levels of psychological resiliency respond after a natural disaster. She obtained anxiety scores, which were measured on a scale of 1-12 with higher numbers meaning more anxiety, from eight individuals who had experienced a natural disaster. She collected these scores 3 weeks after the disaster (M-7.13, s-2.03) and 6 months after the disaster (M-3.5, s-1.6). She expected that the anxiety scores at 6 months would be much lower than at 3 weeks. If sD- 1.30 and you use a two-tailed test with an alpha of.05, is there a difference? Perform the 4 steps of hypothesis testing. 4. Participant Anxiety at 3 Anxiety at 6 Number Weeks Months 10 4 4

Explanation / Answer

here we use t-test with

null hypothesis H0:mean1=mean2 and

alternate hypothesis H1:mean1>mean2

statistic t=(mean1-mean2)/((sp*(1/n1 +1/n2)1/2) =3.97

and sp2=((n1-1)s12+(n2-1)s22)/n and with df is n=n1+n2-2=8+8-2=14

since one-tained p-value =0.0007 is less than the alpha=0.05, so we reject null hypothesis and conclude that there is lower in anxiety level from 3 weeks to 6 month

following information has been generated using ms-excel

t-test sample mean s s2 n (n-1)s2 3weeks 7.13 2.03 4.1209 8 28.8463 6month 3.5 1.6 2.56 8 17.92 difference= 3.63 6.6809 16 46.7663 sp2= 3.34 sp= 1.83 SE= 0.91 t= 3.97 one tailed p-value= 0.0007

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