The intelligence quotients (IQs) of 16 students from one area of a city showed a mean of 107 and a standard deviation of 10, while the IQs of 14 students from another area of the city showed a mean of 112 and a standard deviation of 8. Use alpha = 0.01. What is the pooled standard deviation?

Lexi Mcneil

Lexi Mcneil

Answered question

2022-07-16

The intelligence quotients (IQs) of 16 students from one area of a city showed a mean of 107 and a standard deviation of 10, while the IQs of 14 students from another area of the city showed a mean of 112 and a standard deviation of 8. Use alpha = 0.01. What is the pooled standard deviation?

Answer & Explanation

wintern90

wintern90

Beginner2022-07-17Added 12 answers

n 1 = 16
n 2 = 14
x 1 ¯ = 107
x 2 ¯ = 112
s 1 = 10
s 2 = 8
Pooled standard deviation is defined as an estimate of standard deviation when different groups are assumed to have the same standard deviation.
The pooled variance is given by:
S p 2 = ( n 1 1 ) s 1 2 + ( n 2 1 ) s 2 2 n 1 + n 2 2 = ( 16 1 ) 10 2 + ( 14 1 ) 8 2 16 + 14 2 = 2332 28 = 83.2857
The pooled sd is given by:
s d = 83.2857 = 9.1261
Darian Hubbard

Darian Hubbard

Beginner2022-07-18Added 7 answers

Nice

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