The Minnesota Multiphasic Personality Inventory (MMPI) is a test used to quantif

Question

The Minnesota Multiphasic Personality Inventory (MMPI) is a test used to quantify types of personalities and psychopathologies in adults. Each personality or psychopathology is ranked on a scale from 0 (lowest) to 100 (highest), and the test is scaled in such a way that the population mean should be 50 A general personality study was done of 10 adults who suffer from amnesia (memory loss), and these 10 adults were given the MMPI. One question of interest is whether or not those who suffer from amnesia also tend to show higher symptoms of depression than we would expect from the general public. The average depression score on the MMPI for adults in the general population is 50. The scores for the 10 people in this study are listed below 64 52 56 56 52 58 51 54 63 49 We would like to test to see if there is evidence that the mean depression score for adults with amnesia is significantly greater than 50, Let 0.01 A)The appropriate null/alternative hypothesis pair for this study is: Ho: 50; Ha: 112 50 Ho: x50; Ha: x > 50 Ho: 11-50; Ha: > 50 Ho: = 50; Ha: 50 Ho: x 50; Ha: x > 50 Ho: 50 Ho: 50; Ha: > 50 Ho:

Explanation / Answer

Using Minitab output.

One-Sample T: score

Test of mu = 50 vs > 50

95% Lower
Variable N Mean StDev SE Mean Bound T P
score 10 55.50 4.99 1.58 52.60 3.48 0.003

A)

Formulating the null and alternative hypotheses,              
              
Ho:   u   <=   50  
Ha:    u   >   50
              

B)

X = sample mean = 55.5

c)

s = standard deviation =    4.99   
  

d)

SE = s / sqrt(n) = 1.58

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E)

As we can see, this is a    right   tailed test.      
              
df = n - 1 =    9          
              
Getting the test statistic, as              
              
X = sample mean =    55.5   
uo = hypothesized mean =    50          
n = sample size =    10          
s = standard deviation =    4.99
              
Thus, t = (X - uo) * sqrt(n) / s =    3.48

F)

Also, the p value is              
              
p =    0.0000  

g)

As P < 0.05, we REJECT HO.

Hence, it is

Reject Ho: we can conclude that MMPI depression scores for adults with amnesia are, on average, greater than 50. [5th OPTION is correct]

Hope this will be helpful to you. Thanjks and God Bless you :-)

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