Answer:
We accept H₀. We don´t have enough evidence to support the difference between the two means
Step-by-step explanation:
Group 1 : Comunity College
Sample:
size : n₁ = 54
Sample mean x₁ = 947
Sample standard deviation s₁ = 254
Group 2 : Local University
Sample
size : n₂ = 66
Sample mean : x₂ = 1011
Sample standard deviation s₂ = 87
Significance level α = 0,05 α = 5 % CI = 95 %
Both samples are with n> 30 so we can use z table for the test
from z-table we find z(c) = 1,96
The problem statement establishes to run a hypothesis test to determine if the means are statistically the same ( or different) then we use two-tail-test
Hypothesis Test
Null Hypothesis H₀ x₁ - x₂ = 0 or x₁ = x₂
Alternative hypothesis Hₐ x₁ - x₂ ≠ 0 or x₁ ≠ x₂
To calculate
z(s) = ( x₁ - x₂ ) / √ s₁²/n₁ + s₂²/n₂ )
z(s) = 947 - 1011 / √ (254)²/54 + (87)² / 66
z(s) = - 64 /√ 1194,74 + 114,68
z(s) = - 64 / 36,185
z(s) = - 1,77
Comparing modules of |z(c)| and |z(s)|
z(s) < z(c)
Then z(s) is in the acceptance region we accept H₀ . There is not enough evidence to support differences in the means of the two groups
