Download Two-Sample Intervals - Washburn High School

Two-Sample Intervals
1. The distribution of IQ scores for boys in a large high school are known to follow a Normal
distribution with unknown mean  B and known standard deviation  B  12 . The distribution of IQ
scores for the girls in the school is known to follow a Normal distribution with unknown mean  G
and known standard deviation  G  15 . A simple random sample of 10 boys and an SRS of 13 girls
are drawn independently from the respective populations and the sample means are calculated. The
sample mean for the boys is x B = 102.5 and the sample mean for the girls is x G = 103.2.
Construct and interpret a 90% confidence interval for  B   G .
P: Identify the populations of interest and the parameters you want to estimate.
A: Verify the assumptions/conditions.

Random.

Normal.

Independent.
N: Name the appropriate inference procedure.
I: Carry out the inference procedure. Carry out the interval.
C: State your conclusion in the context of the problem.
2. A farmer wants to determine how much better this new brand of fertilizer (Brand A) is compared to
the old one (Brand B). He decides to divide his field into 1000 plots. He randomly selects 30 plots to
receive Brand A and randomly selects 40 plots to receive Brand B. After this process, if the same
plot comes up in both samples he throws it out of each sample and reselects a new plot for each
brand. This continues until he has 30 plots that will receive Brand A, 40 plots that will receive Brand
B, and 30 plots that will not be a part of his study. At the end of the season he compares the yields
between the brands. He finds that Brand A produced yields with mean x A = 20 bushels per plot with
s A = 3.5, while Brand B produced yields with mean x B = 18.5 bushels per plot with s B = 2.1.
Construct and interpret a 99% confidence interval for
.