Question

Many high school students take the AP tests in different subject areas. In 2007, of the 144,796 students who took the biology test 84,199 of them were female. In that same year, of the 211,693 students who took the calculus AB test 102,598 of them were female. Is there enough evidence to show that the proportion of female students taking the biology test is higher than the proportion of female students taking the calculus AB test? Test at the 5% level.

iv. Determine Pbiology and Pcalculus (enter both in decimal form to the nearest ten thousandth)

v. Let Pbiology=P1 and Pcalculus=P2 (enter in decimal form to the nearest ten thousandth)

vii. Calculate and enter test statistic (enter in decimal form to the nearest ten thousandth)

vii. Using tables, calculator, or spreadsheet: Determine and enter p-value corresponding to test statistic. (enter in decimal form to the nearest ten thousandth)

viii. Comparing p-value and a value, which is the correct decision to make for this hypothesis test?

A. Reject H0

B. Fail to reject H0

C. Accept H0

D. Accept HA

ix. Select the statement that most correctly interprets the result of this test:

A. The result is statistically significant at .05 level of significance. Evidence supports the claim that the proportion of female students taking the biology test is more than the proportion of female students taking the calculus AB test.

B. The result is statistically significant at .05 level of significance. There is not enough evidence to show that the proportion of female students taking the biology test is more than the proportion of female students taking the calculus AB test.

C. The result is not statistically significant at .05 level of significance. There is not enough evidence to show that the proportion of female students taking the biology test is more than the proportion of female students taking the calculus AB exam.

D. The result is not statistically significant at .05 level of significance. Evidence supports the claim that the proportion of female students taking the biology test is less than the proportion of female students taking the calculus AB test.

Answer 1

Given that,
sample one, x1 =84199, n1 =144796, p1= x1/n1=0.582
sample two, x2 =102598, n2 =211693, p2= x2/n2=0.485
null, Ho: p1 = p2
alternate, H1: p1 > p2
level of significance, α = 0.05
from standard normal table,right tailed z α/2 =1.645
since our test is right-tailed
reject Ho, if zo > 1.645
we use test statistic (z) = (p1-p2)/√(p^q^(1/n1+1/n2))
zo =(0.582-0.485)/sqrt((0.524*0.476(1/144796+1/211693))
zo =56.862
| zo | =56.862
critical value
the value of |z α| at los 0.05% is 1.645
we got |zo| =56.862 & | z α | =1.645
make decision
hence value of | zo | > | z α| and here we reject Ho
p-value: right tail - Ha : ( p > 56.8619 ) = 0
hence value of p0.05 > 0,here we reject Ho
ANSWERS
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iv.
Pbiology and Pcalculus
biology test 84,199 of them were female
the calculus AB test 102,598 of them were female.
v.
Pbiology (p1= x1/n1=0.582)
Pcalculus (p2= x2/n2=0.485)
vi.
null, Ho: p1 = p2
alternate, H1: p1 > p2
vii.
test statistic: 56.862
critical value: 1.645
viii.
decision: reject Ho
p-value: 0
ix.
option:A
we have enough evidence to support the claim that the proportion of female students taking the biology test is higher than the proportion of female students taking the calculus AB test