On the first day of term we carried out an experiment, here you will anlayse the

Question

On the first day of term we carried out an experiment, here you will anlayse the data from the experiment. Participants were asked to separate out 40 coins into four bundles (there were 10 1c coins, 10 2c coins, 10 5c coins and 10 10c coins). The randomly selected first group of 9 participants were asked to separate out the coins using both hands. The second group of 10 participants were asked to separate out the coins using only a single hand and to then repeat the process with both hands. The time it took each participant to separate the coins was recorded. The data:

Group 1 Group 2

2 hands 1 hand 2 hands

35 26 22

18   26 21

28 35 30

27 38 26

21 29 22

29 50 25

24 38 17

23 26 19

24 41 23

36 23

Is there evidence that it is quicker to separate coins using two hands compared with only one? Conduct an appropriate hypothesis test(s) to address this question.

Explanation / Answer

To find evidence differnce of time was taken as a variable. If it is greater than zero then it is quicker to separate by two hands.

H0: D<=0

H1: D> 0

t test has to be performed as sample size is less than 30

Mean of Difference = 11.7

Sample Standard Deviation = 7.44

t = 11.7/(7.44/sqrt(10)) = 4.97

Critical value of t is calculated with 95% confidence or alpha of 0.05 from standard t table

Degree of freedom = 10-1 = 9

t(critical) = 1.833

Since t > t(critical) we reject null hypothesis and accept alternate hypothesis, which means time taken by two hands is lesser than that of time taken by one hand

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