The above study read: A study was conducted among adolescents with recent cancer
ID: 3319705 • Letter: T
Question
The above study read:
A study was conducted among adolescents with recent cancer diagnoses who participated in a six week intervention that was designed to enhance their coping skills. Prior to their enrollment, participants’ levels of resilience were measured via a 30 item, 5–point Likert–scale. Higher scores are associated with higher levels of resilience. At pre–test, resilience scores were normally distributed (mean=85, SD=2.5).
Upon conclusion of the above study, participants’ levels of resilience were measured once again (mean=90, SD=5.5).
a. Within what range of two scores below the mean did 34% of participants score? Show all your calculations.
b. What is the associated score for a participant whose score was 3SD below the mean? Show all your calculations.
c. Within what range of scores fell 2SD below and above the mean? Show all your calculations.
d. Within what range of scores fell between 1 SD and 3 SD above the mean? Show all your calculations.
e. In which distribution of resilience scores (pre–test or post–test) are scores more heterogeneous? Provide a brief rationale for your response.
Explanation / Answer
Answer
a. Within what range of two scores below the mean did 34% of participants score? Show all your calculations.
As the distribution is Normal Z value for 34% below the mean is -0.41
Pre Test : Mean 85 SD 2.5
Hence value of Score X satisfies (X-85)/2.5 = -0.41
=> X= 85-2.5*0.41 =83.975
Post Test : Mean 90 SD 5.5
Hence value of Score X satisfies (X-90)/5.5 = -0.41
=> X= 90-5.5*0.41 =87.745
b. What is the associated score for a participant whose score was 3SD below the mean? Show all your calculations.
Z value = -3 Hence score X will satisfy
For Pretest (X-85)/2.5 =3 => X= 85 -2.5*3 = 85-7.5 = 77.5
Hence Score participant below 3SD for Pretest is 77.5
For Posttest (X-90)/5.5 =3 => X= 90 -5.5*3 = 90-16.5 = 73.5
Hence Score participant below 3SD for Posttest is 73.5
c. Within what range of scores fell 2SD below and above the mean? Show all your calculations.
For Pre test
Score range below above 2SD is
85 +/- 2.5*2 => 85+/-5 >80 to 90
For Post test
Score range below above 2SD is
90 +/- 5.5*2 => 90+/-11 >79 to 101
d. Within what range of scores fell between 1 SD and 3 SD above the mean? Show all your calculations.
Pre Teat
Score range between 1SD and 3 SD is
85 + 2.5*1 and 85 +2.5*3 => 85+2.5 to 85+7.5>87.5 to 92.5
For Post test
Score range below above 2SD is
90 + 5.5*1 to 90+5.5*3 => 90+5.5 to 90+16.5 >95.5 to 106.5
e. In which distribution of resilience scores (pre–test or post–test) are scores more heterogeneous? Provide a brief rationale for your response.
Distribution of Post Test score is more heterogeneous . This is because in Post test though there is an increase in average , there is a increase in standard deviation indicating lowest score is lower than pre test and hisgest score is also higher than pre test . This results in higher heterogeneity.
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