Question

Solve in steps

The mean yearly salary for high school teachers in Texas is $48,723. Suppose that a random sample of 50 teachers in a specific district has a mean offer of $49,840 and a standard deviation of $3700. Do the sample data provide strong support for the claim that mean salary for the district is higher than the state average? Test the relevant hypotheses using a = 0.05

Step 1: Null Hypothesis and Alternative Hypothesis

Step 2: Value for alpha

Step 3: Value for N, Value for xBar, Value for S(standard deviation), Value for Test Statistic T and, P value

Step 4: Reject or Not Reject the Null hypothesis

Answer 1

To Test :-

H0 :-

H1 :-  

Test Statistic :-


t = 2.1347

Test Criteria :-
Reject null hypothesis if

= 2.1347 > 1.677
Result :- Reject null hypothesis

Decision based on P value
P - value = P ( t > 2.1347 ) = 0.0189
Reject null hypothesis if P value <    level of significance
P - value = 0.0189 < 0.05 ,hence we reject null hypothesis
Conclusion :- Reject null hypothesis

There is sufficient evidence to support the claim that mean salary for the district is higher than the state average.