In: Statistics and Probability
Many high school students take the AP tests in different subject areas. In 2007, of the 143044 students who took the AP biology exam 76712 of them were female. In that same year, of the 211993 students who took the AP calculus AB exam 100106 of them were female. Is there enough evidence to show that the proportion of AP biology exam takers who are female is higher than the proportion of AP calculus AB exam takers who are female?
a) Test at the 5% level
b) Compute a 90% confidence interval for the difference in
proportions.
Use the steps of PHANTOMS for the hypothesis test.
For the confidence interval you do not need to do all the steps of PANIC since you did some of them already in PHANTOMS.
You just need to do the NIC of PANIC.
Part a.) HYPOTHESIS TEST
P: Parameter
What is the correct parameter symbol and wording for population
1?
Select an answer p̂₁ N₁ n₁ p₁ μ? X̄
μ₁ = Select an answer A randomly selected student who
took the AP biology test that is female The percentage of all
students who took the AP biology test that are female A randomly
selected student who took the AP biology test 143044 randomly
selected students who took the AP biology test All students who
took the AP biology test The percentage of 143044 randomly selected
students who took the AP biology test that are female All students
who took the AP biology test that are female Whether or not a
randomly selected student who took the AP biology test is
female
What is the correct parameter symbol and
wording for population 2?
Select an answer μ? p̂₂ N₂ μ₂ p₂ X̄₂
n₂ = Select an answer All students who took the AP
calculus AB test that are female The percentage of all students who
took the AP calculus AB test that are female All students who took
the AP calculus AB test A randomly selected student who took the AP
calculus AB test The percentage of 211993 randomly selected
students who took the AP calculus AB test that are female A
randomly selected student who took the AP calculus AB test that is
female Whether or not a randomly selected student who took the AP
calculus AB test is female 211993 randomly selected students who
took the AP calculus AB test
H: Hypotheses
Fill in the correct null and alternative hypotheses:
H0:H0: Select an answer μ₁ - μ₂ p₁ - p₂ X̄₁ - X̄₂ N₁ - N₂ p̂₁ - p̂₂
n₁ - n₂ μ? ? > ≥ = ≠ ≤ <
HA:HA: Select an answer μ₁ - μ₂ n₁ - n₂ X̄₁ - X̄₂ p̂₁ - p̂₂ N₁ - N₂
p₁ - p₂ μ? ? ≠ ≥ = > < ≤
A: Assumptions
Since Select an answer quantitative qualitative information was collected from each object, we need to check the following conditions:
Check all that apply.
Check those assumptions:
x1x1 = which is ? ≥ ≠ = < > ≤
x2x2 = which is ? > ≥ < ≤ = ≠
n1−x1n1-x1 = which is ? ≥ = < ≠ >
≤
n2−x2n2-x2 = which is ? = ≤ > < ≠
≥
Population sizes are not given.
We will assume that N1N1 >= 20(n1)n1) and N2N2 >= 20(n2)n2)
N: Name the test
The conditions are met to use a Select an answer T-Test Paired
T-Test 2-Proportion Z-Test 2-Sample T-Test 1-Proportion
Z-Test .
T: Test Statistic
The symbol and value of the random variable (to 4 decimal places) on this problem are as follows:
Select an answer n₁ - n₂ N₁ - N₂ μ₁ -
μ₂ p₁ - p₂ μ? p̂₁ - p̂₂ X̄₁ - X̄₂ =
Pooled Sample proportion of ˆpp^ is as follows:
(Leave your answer in FRACTION form and
use this fraction form in the set up of the test statistic)
ˆpp^ = x1+x2n1+n2x1+x2n1+n2 =
(( ++ )) /(/( ++ )=)=
Set up the formula for the test statistic with EXACT FRACTIONS
or given decimal values for each box:
z=ˆp1−ˆp2√ˆp(1−ˆp)(1n1+1n2)=z=p^1-p^2p^(1-p^)(1n1+1n2)=
(( −- ) / √(( ⋅⋅ (1−(1- )⋅ (1)⋅
(1/ +1+1/ ))=))=
Round final answer from technology to 2 decimal places.
z =
O: Obtain the P-value
Report the final answer to 4 decimal places. It is possible when
rounded that a p-value is 0.0000
P-value =
M: Make a decision
Since the p-value ? = ≤ ≠ ≥ < > , we
Select an answer accept H₀ reject Hₐ fail to reject H₀ fail to
reject Hₐ reject H₀ .
S: State a conclusion
Part b.) CONFIDENCE INTERVAL
N: Name the procedure
The conditions are met to use a Select an answer Paired T-Interval 2-Sample T-Interval T-Interval 2-Proportion Z-Interval 1-Proportion Z-Interval
I: Interval estimate (round endpoints to 3 decimal places)
A % confidence interval for Select an answer p₁ - p₂ μ? μ₁ - μ₂ n₁ - n₂ X̄₁ - X̄₂ p̂₁ - p̂₂ N₁ - N₂ is ( , )
C: Conclusion in context
LicensePoints possible: 58
This is attempt 1 of 2.
a)
paramter
p1 = proportion of AP biology exam takers who are female
p2 = proportion of AP calculus AB exam takers who are female
X1 =76712, n1 = 143044
X2 = 100106 , n2 = 211993
p^ = (X1+x2)/(n1+n2) = 0.49802697
Ho:p1 = p2
Ha: p1 > p2
TS = 37.45
p-value = P(Z >TS) = 0.000
since p-value < alpha
we reject the null hypothesis
we conclude that there is evidence that
proportion of AP biology exam takers who are female is higher than the proportion of AP calculus AB exam takers who are female
b)
90% confidence interval
90% CI is (0.0613,0.0669