Test #2
Step 1
p (sub 1)= True proportion of pins knocked down on the first throw by Hispanic high school students
p (sub 2)= True proportion of pins knocked down on the first throw by non-Hispanic high school students
Ho: p (sub 1)- p (sub 2) = 0
Ha: p (sub 1)- p (sub2) ≠ 0
α= .05
Step 2
Two-sample z test for proportion (p (sub 1)- p (sub 2))
Random- not random; proceed with caution. The groups were picked based on grades.
Normal-
p hat (sub c) = 313+175/ 400+200= (488/600)
n (sub 1) x p hat (sub c)= 400(/8133)= 325.32
n (sub 1) x (1- p hat (sub c))= 400(.1867) = 74.68
n (sub 2) x p hat (sub c)= 200(.8133)= 162.68
n (sub 2) x (1- p hat (sub c))= 200(.1867)= 37.34
Because they are all greater than 10, normality is satisfied
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
z= ((p hat (sub 1)- p hat (sub 2))- (p (sub 1) - p (sub 2))/ square root of ((p hat (sub c) - 1-p hat (sub c)) x (1/ n (sub 1) + (1/n(sub 2))
= ((313/400)- (125/200) - 0)/ square root of (488/600 (1- (488/600) (1/400+ 1/200)
=-2.741
P-value= P(z ≠ -2.741) = 2P(z< -2.741) = 2(.006492)= .012986
Step 4
Since 0.012986 < 0.05 (α), we reject Ho at the 5% level. We have evidence to suggest that there is a difference in the true proportions of pins knocked down on the first throw by Hispanic and non-Hispanic high school students.
p (sub 1)= True proportion of pins knocked down on the first throw by Hispanic high school students
p (sub 2)= True proportion of pins knocked down on the first throw by non-Hispanic high school students
Ho: p (sub 1)- p (sub 2) = 0
Ha: p (sub 1)- p (sub2) ≠ 0
α= .05
Step 2
Two-sample z test for proportion (p (sub 1)- p (sub 2))
Random- not random; proceed with caution. The groups were picked based on grades.
Normal-
p hat (sub c) = 313+175/ 400+200= (488/600)
n (sub 1) x p hat (sub c)= 400(/8133)= 325.32
n (sub 1) x (1- p hat (sub c))= 400(.1867) = 74.68
n (sub 2) x p hat (sub c)= 200(.8133)= 162.68
n (sub 2) x (1- p hat (sub c))= 200(.1867)= 37.34
Because they are all greater than 10, normality is satisfied
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
z= ((p hat (sub 1)- p hat (sub 2))- (p (sub 1) - p (sub 2))/ square root of ((p hat (sub c) - 1-p hat (sub c)) x (1/ n (sub 1) + (1/n(sub 2))
= ((313/400)- (125/200) - 0)/ square root of (488/600 (1- (488/600) (1/400+ 1/200)
=-2.741
P-value= P(z ≠ -2.741) = 2P(z< -2.741) = 2(.006492)= .012986
Step 4
Since 0.012986 < 0.05 (α), we reject Ho at the 5% level. We have evidence to suggest that there is a difference in the true proportions of pins knocked down on the first throw by Hispanic and non-Hispanic high school students.