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 H_O 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

Solution :

Given that ,

= 57.2  

= 54.8

s = 4.3

n = 25

The null and alternative hypothesis is ,

H₀ :   = 57.2

H_a :    57.2

This is the two tailed test .

Standard error = SE = s / n = 4.3 / 25  = 0.86

The Standard error = SE = 0.86

Test statistic = t

= ( - ) / s / n

= ( 54.8 - 57.2) / 4.3 / 25

= -2.79

The test statistic = -2.79

df = n - 1 = 25 - 1 = 24

P-value = 2 * ( t _{-2.79,24 )}

= 2 * 0.0051

= 0.0102

P-value = 0.0102

= 0.05  

0.0102 < 0.05

P-value <

Reject the null hypothesis .

conclusion : - There is sufficient evidence to test the claim .