Question

The USA has been invaded by a ship of 6 aliens -- well, sort of, they actually just flew here from planet YB54D (known to them simply as "Home") as a part of their search for extraterrestrial life. Our military contained them immediately and we are holding them captive for further study (from this sample of 6 aliens we hope to be able to predict what the rest of their kind -- i.e., their entire population -- will be like). One of the first things we want to assess is their hostility; thus, we send in a psychologist who administers the Buss-Perry Aggression Questionnaire (BPAQ), which rates hostility on a scale of 8 to 40, with higher ratings indicating higher hostility. Their scores are as follows:

Alien 1: 20   Alien 4: 9

Alien 2: 17 Alien 5: 13  

Alien 3: 31 Alien 4: 38  

What would the BPAQ score be of an alien who is 1.5 standard deviations below the mean (round to two decimal places)?

What would the BPAQ score be of an alien who is 1 standard deviation above the mean (round to two decimals)?

Answer 1

The USA has been invaded by a ship of 6 aliens -- well, sort of, they actually just flew here from planet YB54D (known to them simply as "Home") as a part of their search for extraterrestrial life. Our military contained them immediately and we are holding them captive for further study (from this sample of 6 aliens we hope to be able to predict what the rest of their kind -- i.e., their entire population -- will be like). One of the first things we want to assess is their hostility; thus, we send in a psychologist who administers the Buss-Perry Aggression Questionnaire (BPAQ), which rates hostility on a scale of 8 to 40, with higher ratings indicating higher hostility. Their scores are as follows:

Alien 1: 20   Alien 4: 9

Alien 2: 17 Alien 5: 13  

Alien 3: 31 Alien 4: 38  

Descriptive statistics
count	6
mean	21.3333
sample standard deviation	11.0755
sample variance	122.6667
minimum	9
maximum	38
range	29

What would the BPAQ score be of an alien who is 1.5 standard deviations below the mean (round to two decimal places)?

21.3333-1.5*11.0755= 4.72005

=4.72 ( 2 decimals)

What would the BPAQ score be of an alien who is 1 standard deviation above the mean (round to two decimals)?

21.3333+1.0*11.0755= 32.4088

=32.41 ( two decimals)