In: Statistics and Probability

In one school district, there are 89 elementary school (K-5) teachers, of which 18 are male (or male-identifying). In a neighboring school district, there are 102 elementary teachers, of which 17 are male. A policy researcher would like to calculate the 99% confidence interval for the difference in proportions of male teachers.

To keep the signs consistent for this problem, we will calculate all differences as p1−p2. That is, start with the percentage from the first school district and then subtract the percentage from the second district. Failing to do so may end up with “correct” answers being marked as wrong.

Point estimate for the percentage males in the first district:

ˆp1=

Point estimate for the percentage males in the second district:

ˆp2=

Point estimate for the difference in percentages between the two districts:

ˆp1−ˆp2=

Estimate of the standard error for this sampling distribution (distribution of differences):

√ˆp1(1−ˆp1)n1+ˆp2(1−ˆp2)n2=

Critical value for the 99% confidence level:

zc.v.=

99% margin of error:

M.E.=

99% confidence interval:

≤p1−p2≤

Salaries for teachers in a particular elementary school district
are normally distributed with a mean of $44,000 and a
standard deviation of $6,500. We randomly survey ten teachers from
that district.
1.Find the probability that the teachers earn a total of over
$400,000
2.If we surveyed 70 teachers instead of ten, graphically, how
would that change the distribution in part d?
3.If each of the 70 teachers received a $3,000 raise,
graphically, how would that change the distribution in part...

Salaries for teachers in a particular elementary school district
are normally distributed with a mean of $44,000 and a standard
deviation of $6,500. We randomly survey ten teachers from that
district. Find the 85th percentile for the sum of the sampled
teacher's salaries to 2 decimal places.

Salaries for teachers in a particular elementary school district
are normally distributed with a mean of $41,000 and a standard
deviation of $6,100. We randomly survey ten teachers from that
district.
A. Give the distribution of ΣX. (Round your answers to
two decimal places.)
ΣX - N ( , )
B. Find the probability that the teachers earn a total
of over $400,000. (Round your answer to four decimal places.)
C. Find the 80th percentile for an individual
teacher's salary....

Salaries for teachers in a particular elementary school district
are normally distributed with a mean of $46,000 and a standard
deviation of $4,900. We randomly survey ten teachers from that
district. (Round your answers to the nearest dollar.)
(a) Find the 90th percentile for an individual
teacher's salary.
(b) Find the 90th percentile for the average teacher's
salary.

7.75 p. 428
Salaries for teachers in a particular
elementary school district are normally distributed with a mean of
$44,000 and a standard deviation of $6,500. We randomly survey ten
teachers from that district.
a. In words, X = ______________
b. X ~ _____(_____,_____)
c. In words, ΣX = _____________
d. ΣX ~ _____(_____,_____)
e. Find the probability that the
teachers earn a total of over $400,000.
f. Find the 90th percentile for an
individual teacher's salary.
g. Find the...

Within a school district, students were randomly assigned to
one of two Math teachers - Mrs. Smith and Mrs. Jones. After the
assignment, Mrs. Smith had 30 students, and Mrs. Jones had 25
students. At the end of the year, each class took the same
standardized test. Mrs. Smith's students had an average test score
of 78, with a standard deviation of 10; and Mrs. Jones' students
had an average test score of 85, with a standard deviation of 15....

A researcher claims that the mean of the salaries of elementary
school teachers is greater than the mean of the salaries of
secondary school teachers in a large school district. The mean of
the salaries of a random sample of 26 elementary school teachers is
$48,250 and the sample standard deviation is $3900. The mean of the
salaries of 24 randomly selected secondary school teachers is
$45,630 with a sample standard deviation of $5530. At ? = 0.05, can
it...

A study was conducted to estimate the difference in the mean
salaries of elementary school teachers from two neighboring states.
A sample of 10 teachers from the Indiana had a mean salary of
$28,900 with a standard deviation of $2300. A sample of 14 teachers
from Michigan had a mean salary of $30,300 with a standard
deviation of $2100. Determine a 95% confidence interval for the
difference between the mean salary in Indiana and Michigan.(Assume
population variances are different.)
*Include...

A study was conducted to determine if the salaries of elementary
school teachers from two neighboring districts were equal. A sample
of 15 teachers from each district was randomly selected. The mean
from the first district was $28,900 with a standard deviation of
$2300. The mean from the second district was $30,300 with a
standard deviation of $2100. Assume the samples are random,
independent, and come from populations that are normally
distributed. Construct a 95% confidence interval for μ1 -...

Many elementary school students in a school district currently
have ear infections. A random sample of children in two different
schools found that 21 of 42 at one school and 15 of 35 at the other
had this infection. Conduct a test to answer if there is sufficient
evidence to conclude that a difference exists between the
proportion of students who have ear infections at one school and
the other. Find the test statistic.

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