Question

T-Test Problems (show your work) (NO HAND WRITING ITS HARD TO READ)

A researcher wishes to determine if a particular drug affects pilot reaction time to air traffic controller instructions. The researcher has 10 pilots. The pilots are observed in normal performance and their reaction times are recorded. Then the pilots are administered the drug, observed again, and their reaction times are recorded. The expectation is that the drug will reduce reaction time.

Pilot	Trial 1 Time (sec)	Trail 2 Time (sec)
A	.83	.69
B	.74	.71
C	.82	.79
D	.86	.87
E	.66	.65
F	.63	.68
G	.81	.67
H	.77	.72
I	.73	.71
J	.69	.65

Conduct a t test using the five-step hypothesis testing process

Answer 1

In the given problem, we are to test if the particular drug reduces pilot reaction time to air - traffic controller instructions. In order to do that, we construct our null and alternative hypotheses as:

H0: mu_d = 0 vs. H1: mu_d > 0

where mu_d is the unknown population average of the difference between the two trial groups without and with the drug.

The required test - statistic for this hypotheses is T = (d - mu_d0)/(sd/((n)^0.5)) ~ t (n-1) under H0.

Where d = mean of the sample differences; mu_d0 = hypothesized value of the population average; sd = standard deviation of the differences and n= sample size.

We reject H0 iff T(observed) > t(alpha, n-1); where t(alpha, n-1) is the upper alpha point of a Student's t - distribution with (n-1) degrees of freedom.

Here, T(observed) = 2.114722 and t(alpha, n-1) = 1.833113.

As T(observed) > T(alpha, (n-1)), we reject H0 and conclude on the basis of the given sample measures and 5% level of significance that there is sufficient evidence to conclude that the usage of drugs does reduce the reaction time of the pilots.

(The answers are obtained using R-software. The code and the output are attached below for verification).