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.

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
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2.If we surveyed 70 teachers instead of ten, graphically, how
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3.If each of the 70 teachers received a $3,000 raise,
graphically, how would that change the distribution in part...

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Salaries for teachers in a particular elementary school district
are normally distributed with a mean of $41,000 and a standard
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A. Give the distribution of ΣX. (Round your answers to
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ΣX - N ( , )
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Salaries for teachers in a particular elementary school district
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A study was conducted to estimate the difference in the mean
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Salaries for teachers in a particular elementary school district
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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
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A) Find the 90th percentile for an individual
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: 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...

A study was conducted to determine if the salaries of elementary
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7.75 p. 428
Salaries for teachers in a particular
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a. In words, X = ______________
b. X ~ _____(_____,_____)
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d. ΣX ~ _____(_____,_____)
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teachers earn a total of over $400,000.
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