A very scrupulous friend wishes to see if money is a better motivator than fear:

Question

A very scrupulous friend wishes to see if money is a better motivator than fear: and designs an entirely ethical matched pairs experiment to test this. After a few trials runs on a 400m track, participants were offered a chance to win S500 if they beat their previous best time. They were also timed running while being chased by two large, scary dogs. The difference between each person's money motivated time and fear motivated time (specifically, run time[money] = run time [fear]) is then calculated from the sample. 3.a) A sample of 33 individuals finds that that when motivated by money, people ran slightly faster with a sample average time difference of = 1.25 seconds and a standard deviation of 4.4 seconds. Calculate a 99% confidence interval for the true average run time difference. 3.b) What does it mean to say you have 99% confidence in the interval found in 3.a? 3.c) State the null and alternative hypotheses in both words and mathematical notation, to to test the claim, "Is money a better motivator than fear?" 3.d) Calculate a test statistic for testing the hypothesis in 3.c, using the data found in 3.a. 3.e) Based on your test statistic found in 3.d, what is the p-value associated with this test? 3.f) Based on the p-value found in 3.e, testing at a 5% level what do you conclude about your null and alternative hypotheses? What does this mean in terms of the original question of interest?

Explanation / Answer

Part-a

Degree of freedom=33-1=32

Critical t= 2.7385

99% confidence interval =xbar±t*s/sqrt(n)

=-1.25± 2.7385*4.4/sqrt(33)

=(-3.347531308     0.847531308)

Part-b

We are 99% confident that the average time difference will li in this interval

Part-c

Null hypothesis H0: =0

Alternative hypothesis H0: <0

Part-d

Test statistic t=( xbar-278)/(s/sqrt(n))

=(-1.25-0)/(4.4/sqrt(33))

=-1.631978025

Part-e

p-value=P(t<-1.6320)

=0.056243918

Part-f as p-value>0.05, we do not reject the null hypothesis and conclude that money is not better motivator than fear.

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