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.

Salaries for teachers in a particular elementary school district
are normally distributed with a mean of $46,000 and a standard
deviation of $4,500. 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.

Salaries for teachers in a particular elementary school district
have a mean of $44,000 and a standard deviation of $6,500. We
randomly survey 36 teachers from that district.
Why can we say the sampling distribution of mean salaries for
teachers in this district is approximately normal?
Find the probability that the mean salary is less than
$43,000.
Find the probability that the mean salary is between $45,000
and $47,000.

Salaries for teachers in a particular elementary school district
are normally distributed with a mean of $42,000 and a standard
deviation of $5,700. 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.
$ =

Salaries for teachers in a particular elementary school district
are normally distributed with a mean of $44,000 and a standard
deviation of $6,300. 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.
A typical adult has an average IQ score of 105 with a standard
deviation of 20. If 19 randomly selected adults are...

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...

2. An elementary school employs 20 teachers; 12 are women and 8
are men. Two teachers are selected at random to meet the governor.
Is this selection done with or without replacement?
a) What is the chance that both are women?
b) What is the chance that at least one is a women?
c) What is the chance that both are the same gender?

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