Question

9.1.2

Many high school students take the AP tests in different subject areas. In 2007, of the 144,796 students who took the biology exam 84,199 of them were female. In that same year, of the 211,693 students who took the calculus AB exam 102,598 of them were female ("AP exam scores," 2013). Estimate the difference in the proportion of female students taking the biology exam and female students taking the calculus AB exam using a 90% confidence level.

a.) State the random variables and the parameters in words.

   =

=

=

=

b.)          State and check the assumptions for confidence interval:

c.)           Find the sample statistics and confidence interval

Sample Proportion:

Confidence Interval:

d.)          Statistical Interpretation:

e.)          Real World Interpretation:

Answer 1

a.) State the random variables and the parameters in words.

The variables are female students who took the biology exam and female students who took the calculus AB exam.

b.)          State and check the assumptions for confidence interval:

• The sampling method for each population is simple random sampling.
• The samples are independent.
• Each sample includes at least 10 successes and 10 failures.
• Each population is at least 20 times as big as its sample.

c.)           Find the sample statistics and confidence interval

Sample Proportion: 0.523991

Confidence Interval: (0.094, 0.100)

d.)          Statistical Interpretation:

We are 90% confident that the true difference in the proportion of female students taking the biology exam and female students taking the calculus AB exam is between 0.094 and 0.100.

e.)          Real World Interpretation:

More female students take the biology exam than the calculus AB exam.

p1	p2	pc
0.5815	0.4847	0.523991	p (as decimal)
84199/144796	102598/211693	0.523991	p (as fraction)
84199	102598	186797	X
144796	211693	356489	n
	0.0968	difference
	0	hypothesized difference
	0.0017	std. error
	0.094	confidence interval 90.% lower
	0.1	confidence interval 90.% upper