The Minnesota Multiphasic Personality Inventory MMPI is a te

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:

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 = 0.05

A)The appropriate null/alternative hypothesis pair for this study is:

Ho: 50; Ha: > 50

Ho: = 50; Ha: > 50  

  Ho: x 50; Ha: x > 50

Ho: 50; Ha: 50

Ho: 50; Ha: < 50

Ho: = 50; Ha: 50

Ho: < 50; Ha: 50

Ho: x = 50; Ha: x > 50

Ho: < 50; Ha: > 50

B) The sample average is:  
    Note: round your answer to the nearest hundredth

C) The sample standard deviation is:  
      Note: round your answer to the nearest hundredth

D) The standard error of the sample average is:  
      Note: round your answer to the nearest hundredth

E) The test statistic for this data set is: t-statistic =  
      Note: Round your answer to the nearest hundredth.

F) The p-value for this study is:  
      Note: express your answer to 4 decimal precision

G) The statistical decision and corresponding English interpretation are:

Reject Ho: we can conclude that MMPI depression scores for adults with amnesia are, on average, less than 50.

FTR Ho: we cannot conclude that MMPI depression scores for adults with amnesia are, on average, different than 50.   

Reject Ho: we can conclude that MMPI depression scores for adults with amnesia are, on average, greater than 50.

Reject Ho: we can conclude that MMPI depression scores for adults with amnesia are, on average, less than 50.

FTR Ho: we cannot conclude that MMPI depression scores for adults with amnesia are, on average, more than 50.

FTR Ho: we cannot conclude that MMPI depression scores for adults with amnesia are, on average, less than 50

FTR Ho: we can conclude that MMPI depression scores for adults with amnesia are, on average, different than 50.

Solution

A)

Formulating the null and alternative hypotheses,              
              
Ho:   u   <=   50  
Ha:    u   >   50 [ANSWER]  
              
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B)

X = sample mean =    52.4   [ANSWER]

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c)

s = standard deviation =    3.533962208      
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d)

SE = s / sqrt(n) = 1.117536974 [ANSWER]

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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 =    52.4          
uo = hypothesized mean =    50          
n = sample size =    10          
s = standard deviation =    3.533962208          
              
Thus, t = (X - uo) * sqrt(n) / s =    2.147579951 [ANSWER, T STATISTIC]          

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F)

Also, the p value is              
              
p =    0.030136752   [ANSWER, P VALUE]      
              
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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. [3RD OPTION]