In: Statistics and Probability

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 be concluded that the mean of the salaries of elementary school teachers is greater than the mean of the salaries of secondary school teachers?

To Test :-

H0 :- µ1 = µ2

H1 :- µ1 > µ2

Test Statistic :-

t = (X̅1 - X̅2) / SP √ ( ( 1 / n1) + (1 / n2))

t = ( 48250 - 45630) / 4751.3391 √ ( ( 1 / 26) + (1 / 24 ) )

**t = 1.948**

Test Criteria :-

Reject null hypothesis if t > t(α, n1 + n2 - 2)

Critical value t(α, n1 + n1 - 2) = t( 0.05 , 26 + 24 - 2) =
1.677

t > t(α, n1 + n2 - 2) = 1.948 > 1.677

**Result :- Reject Null Hypothesis**

Decision based on P value

P - value = P ( t > 1.948 ) = 0.0286

Reject null hypothesis if P value < α = 0.05 level of
significance

P - value = 0.0286 < 0.05 ,hence we reject null hypothesis

**Conclusion :- Reject null hypothesis**

There is sufficient evidence to concluded that the mean of the salaries of elementary school teachers is greater than the mean of the salaries of secondary school teachers.

A researcher claims that the variation in the salaries of
elementary school teachers is greater than the variation in the
salaries of secondary school teachers. A random sample of the
salaries of 30 elementary school teachers has a variance of $8,208,
and a random sample of the salaries of 30 secondary school teachers
has a variance of $3,817. At α = 0.05, can the researcher conclude
that the variation in the elementary school teachers’ salaries is
greater than the variation...

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.

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...

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.
$ =

: A researcher is interested in whether salaries for middle
school teachers were less than salaries for nurses in Arkansas. A
statewide salary survey is conducted using random sampling.
The Data Analysis output for the various tests used when
comparing two group means are shown below. The significance level
was .05.
F-Test Two-Sample for Variances
Teachers
Nurses
Mean
45946.07
53365.13
Variance
68256753
86820446
Observations
300
300
df
299
299
F
0.7862
P(F<=f) one-tail
0.0190
F Critical one-tail
0.8265
t-Test: Paired...

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