In: Math
According to published reports, practice under fatigued
conditions distorts mechanisms that govern performance. An
experiment was conducted using
15 college males, who were trained to make a continuous horizontal
right-to-left arm movement from a microswitch to a barrier,
knocking over the barrier coincident with the arrival of a clock
sweephand to the 6 o’clock position. Theabsolute value of the
difference between the times, in milliseconds, that it took to
knock over the barrier and the time for the sweephand to reach the
6 o’clockposition (500 msec) was recorded. Each participant
performed the task five times under prefatigue and postfatigue
conditions, and the sums of the absolute differences for the five
performances were recorded. The data can be found in the folder of
this question.
a) (0.5 point) Read the data into R using read.csv function. Note: Show your codes but not the result/output.
b) (0.5 point) An increase in the mean absolute time difference when the task is performed under postfatigue conditions would support the claim that practice under fatigued conditions distorts mechanisms that govern performance. Assuming the populations to be normally distributed, write the two hypothesis of interest to test this claim.
c) (1 point) Use a suitable test in R to test your hypothesis in (b). Show your codes, output and use α = 0.05.
d) (1 point) Interpret your finding in (c).
data:
Prefatigue,Postfatigue
159,92
93,60
66,216
99,227
34,224
90,92
149,93
59,178
143,135
118,117
75,154
67,220
110,144
58,165
86,101
> t.test(x$V2,x$V1,paired=TRUE,alternative = "greater",conf.level = 0.95)
Paired t-test
data: x$V2 and x$V1
t = 2.5259, df = 14, p-value = 0.01211
alternative hypothesis: true difference in means is greater than
0
95 percent confidence interval:
16.38644 Inf
sample estimates:
mean of the differences
54.13333
d) Clearly, p-value < 0.05 so we conclude that the given data provides sufficient evidence that there is an increase in the mean absolute time difference when the task is performed under postfatigue conditions. Hence this supports the claim that practice under fatigued conditions distorts mechanisms that govern performance.