Question

A pilot training program usually takes an average of 57.2 hours, but new teaching methods were used on the last class of 25 students. The experimental class completion times had a mean of 54.8 hours and a standard deviation of s = 4.3 hours. State HO and H1 and test the claim at the 0.05 significance level that the new teaching techniques reduce the instruction time. Check conditions, compute the standard error, standardize and give the degrees of freedom. Include a sketch, state the p-value followed by your conclusion.

Answer 1

To Test :-

H0 :- µ = 57.2
H1 :- µ < 57.2

Test Statistic :-
t = ( X̅ - µ ) / (S / √(n) )
t = ( 54.8 - 57.2 ) / ( 4.3 / √(25) )
t = -2.7907

Degree of freedom = n - 1 = 25 - 1 = 24

Standard Error = S/√(n) = 0.86

P - value = P ( t > 2.7907 ) = 0.0051

Reject null hypothesis if P value < α = 0.05 level of significance
P - value = 0.0051 < 0.05 ,hence we reject null hypothesis
Conclusion :- Reject null hypothesis

There is sufficient evidence to support the claim that the new teaching techniques reduce the instruction time.