The Minnesota Multiphasic Personality Inventory (MMPI) is a test used to quantif
ID: 3130736 • Letter: T
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:
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 one of the following:
Ho: x 50 Ha: x > 50
Ho: 50; Ha: < 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
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 =
Note: Round your answer to the nearest hundredth.
F) The p-value for this study is:
Explanation / Answer
a)
Formulating the null and alternative hypotheses,
Ho: u <= 50
Ha: u > 50 [ANSWER, OPTION A]
***********************
b)
Using technology,
X = sample mean = 54.9 [ANSWER]
***********************
c)
s = standard deviation = 3.842742077
***********************
d)
The standard error is, as n = 10,
SE = s/sqrt(n) = 1.215181742 [ANSWER]
***********************
e)
Getting the test statistic, as
X = sample mean = 54.9
uo = hypothesized mean = 50
n = sample size = 10
s = standard deviation = 3.842742077
Thus, t = (X - uo) * sqrt(n) / s = 4.032318648 [ANSWER]
************************
f)
As we can see, this is a right tailed test.
df = n - 1 = 9
Hence, the p value is
p = 0.001481311 [ANSWER]
*************************
As P < 0.05, re reject Ho. There is significant evidence at 0.05 level that the mean depression score for adults with amnesia is significantly greater than 50.