test #1
Step 1: Mu (sub 1)= True mean score per frame of Hispanic high school students
Mu (sub 2)= True mean score per frame of non-Hispanic high school students
Ho: Mu (sub 1)- Mu (sub 2)= 0
Ha: Mu (sub 1)- Mu (sub 2)≠ 0
α= .05
Step 2 Two-sample t test for Means (Mu (sub 1)- Mu (sub 2))
Random- not random; proceed with caution. The groups were picked based on grades.
Normal- The data didn't show a Normal distribution and only 1 of the 2 samples was large, so we couldn't use CLT to verify Normality, so we cannot verify Normality and must proceed with caution.
Independent - N (sub 1) ≥ 10(n (sub 1))
N (sub 1) ≥ 10(4)
N (sub 1) ≥ 40
N (sub 2) ≥ 10(n (sub 2))
N (sub 2) ≥ 10(2)
N (sub 2) ≥ 20
We can assume that the population of Hispanic high school students is greater than 40, and that the population of non-Hispanic high school students is greater than 20. Thus, we can assume independence.
Step 3
t= ((x bar (sub1) - x bar (sub2)) - (mu (sub1) - mu (sub 2))) / square root of ((s (sub1)^2 / n (sub 1)) + (s (sub 2)^2 / n (sub2))
= ((15.05 - 18.8) - 0 ) / square root of ((6.2^2 / 40) + (9.58^2 / 20))
= -3.75 / square root of (.961 + 1.04882)
= -3.75 / square root of (2.00982)
= -3.75 / 1.4177
= -2.645
df = 20 - 1
= 19
P-value= P(t≠ -2.645) = 2P(t< -2.645) = 2(.007985) = .01597
Step 4 Since .01597 < .05 (α), we reject Ho at the 5% level. We have sufficient evidence to suggest that there is a difference between the true mean scores per frame of Hispanics and non-Hispanics.
Mu (sub 2)= True mean score per frame of non-Hispanic high school students
Ho: Mu (sub 1)- Mu (sub 2)= 0
Ha: Mu (sub 1)- Mu (sub 2)≠ 0
α= .05
Step 2 Two-sample t test for Means (Mu (sub 1)- Mu (sub 2))
Random- not random; proceed with caution. The groups were picked based on grades.
Normal- The data didn't show a Normal distribution and only 1 of the 2 samples was large, so we couldn't use CLT to verify Normality, so we cannot verify Normality and must proceed with caution.
Independent - N (sub 1) ≥ 10(n (sub 1))
N (sub 1) ≥ 10(4)
N (sub 1) ≥ 40
N (sub 2) ≥ 10(n (sub 2))
N (sub 2) ≥ 10(2)
N (sub 2) ≥ 20
We can assume that the population of Hispanic high school students is greater than 40, and that the population of non-Hispanic high school students is greater than 20. Thus, we can assume independence.
Step 3
t= ((x bar (sub1) - x bar (sub2)) - (mu (sub1) - mu (sub 2))) / square root of ((s (sub1)^2 / n (sub 1)) + (s (sub 2)^2 / n (sub2))
= ((15.05 - 18.8) - 0 ) / square root of ((6.2^2 / 40) + (9.58^2 / 20))
= -3.75 / square root of (.961 + 1.04882)
= -3.75 / square root of (2.00982)
= -3.75 / 1.4177
= -2.645
df = 20 - 1
= 19
P-value= P(t≠ -2.645) = 2P(t< -2.645) = 2(.007985) = .01597
Step 4 Since .01597 < .05 (α), we reject Ho at the 5% level. We have sufficient evidence to suggest that there is a difference between the true mean scores per frame of Hispanics and non-Hispanics.