You want to know whether your sample has significantly highe

You want to know whether your sample has significantly higher IQ scores than the general population. You know that for the test you used, the average IQ score is 100 and the standard deviation is 15.

IQ

a. Calculate the appropriate test BY HAND to determine whether your sample has significantly higher IQ scores (IQ) than the general population. (2 pts)

b. If applicable, also determine the size of the effect (.5 pt).

c. Report a formal conclusion explaining your findings, including both part A and B. (1.5 pts).

  101  

  123  

  108  

  111  

  98  

  97  

  116  

  114  

  108  

  120  

Solution

a.
Set Up Hypothesis
Null H0: U=100
Alternate H1: U>100
Test Statistic
Population Mean(U)=100
Given That X(Mean)=109.6
Standard Deviation(S.D)=15
Number (n)=10
we use Test Statistic (Z) = x-U/(s.d/Sqrt(n))
Zo=109.6-100/(15/Sqrt(10)
Zo =2.0239
| Zo | =2.0239
Critical Value
The Value of |Z | at LOS 0.051% is 1.64
We got |Zo| =2.0239 & | Z | =1.64
Make Decision
Hence Value of | Zo | > | Z | and Here we Reject Ho
P-Value : Right Tail - Ha : ( P > 2.0239 ) = 0.0215
Hence Value of P0.051 > 0.0215, Here we Reject Ho

b.
Effect size: x1-x2/S = 109.6-100/15 = 0.64
c)
we can conclude that sample has significantly higher IQ scores than the general population