Wiisports: baseball
We wanted to test if the difference between proportions of home runs hit by people who own a Nintendo Wii is higher with those who don't.
Step 1: state
P1= the true proportion of homeruns hit by people who have WIIs
P2= the true proportion of homeruns hit by people who don’t have WIIs
Ho= P1- p2= 0
Ha= P1- P2 > 0
α= 0.05
P2= the true proportion of homeruns hit by people who don’t have WIIs
Ho= P1- p2= 0
Ha= P1- P2 > 0
α= 0.05
step 2: plan
2 Sample Proportions for p1 - p2
Random: Not random since the sample isn’t an SRS, proceed with caution Normality:
Normal:
n1Pc ≥ 10
n (1 - Pc) ≥ 10
n2Pc ≥ 10
n (1- Pc) ≥ 10
30(0.3143) = 9.429 ≥ 10
30 ( 1 - 0.3143) = 20.57 ≥ 10
40(0.3143) = 12.57 ≥ 10
40( 1 - 0.3143) = 27.43 ≥ 10
Although the conditions for normality aren't met for all, we should proceed with caution.
Pc = 22/70 = 0.3143
Independence: We must assume that there are more than N1≥10(4)= 40 people who own Wii. We must assume that the true proportion of people who don’t own Wii is N2≥10(3)= 30.
Random: Not random since the sample isn’t an SRS, proceed with caution Normality:
Normal:
n1Pc ≥ 10
n (1 - Pc) ≥ 10
n2Pc ≥ 10
n (1- Pc) ≥ 10
30(0.3143) = 9.429 ≥ 10
30 ( 1 - 0.3143) = 20.57 ≥ 10
40(0.3143) = 12.57 ≥ 10
40( 1 - 0.3143) = 27.43 ≥ 10
Although the conditions for normality aren't met for all, we should proceed with caution.
Pc = 22/70 = 0.3143
Independence: We must assume that there are more than N1≥10(4)= 40 people who own Wii. We must assume that the true proportion of people who don’t own Wii is N2≥10(3)= 30.
Step 3: do
z = 0.5667 - 0.125 / √ 0.3143 (1-0.3143) (1/30 + 1/40)
= 3.939
P(z > 3.939) = normalcdf ( 3.939, 1e99, 0, 1)
= 0.00004093
= 3.939
P(z > 3.939) = normalcdf ( 3.939, 1e99, 0, 1)
= 0.00004093
step 4: Conclude
Since our P-value of 0.00004093 is less than our Alpha Level of 0.05, we reject H0 at the 5% level. We have evidence to conclude that people who have Wii's have a better proportion of hitting home runs than people who don't have Wii's.