##### Question

In: Statistics and Probability

# A researcher claims that the mean of the salaries of elementary school teachers is greater than...

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?

## Solutions

##### Expert Solution

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.

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