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An instrument panel is being designed to control a complex industrial process. It will be necessary to use
both hands independently to operate the panel. To help with the design it was decided to time a number of
operators, each carrying out the same task once with the left hand (LH) and once with the right hand (RH).
The times, in seconds, were as follows. Calculate the product moment correlation coefficient between the two
variables and interpret the results. [6 marks]
Operator A B C D E F G H I J K
LH 49 58 63 42 27 55 39 33 72 66 50
RH 34 37 49 27 49 40 66 21 64 42 37

Respuesta :

Step-by-step explanation:

To calculate the product moment correlation coefficient between the left hand (LH) and right hand (RH) times, we can use the formula:

r = Σ((LH - LH_avg) * (RH - RH_avg)) / √(Σ(LH - LH_avg)^2 * Σ(RH - RH_avg)^2)

Let's calculate it step by step:

1. Calculate the average LH and RH times:

LH_avg = (49 + 58 + 63 + 42 + 27 + 55 + 39 + 33 + 72 + 66 + 50) / 11

RH_avg = (34 + 37 + 49 + 27 + 49 + 40 + 66 + 21 + 64 + 42 + 37) / 11

2. Calculate the numerator:

LH_diff = (49 - LH_avg), (58 - LH_avg), ..., (50 - LH_avg)

RH_diff = (34 - RH_avg), (37 - RH_avg), ..., (37 - RH_avg)

Multiply LH_diff and RH_diff for each operator and sum them up.

3. Calculate the denominator:

Calculate the squared differences for LH_diff and RH_diff for each operator and sum them up.

4. Divide the numerator by the square root of the denominator.

The resulting value will be the product moment correlation coefficient (r) between LH and RH times. The interpretation of the coefficient will indicate the strength and direction of the relationship between the variables. A value close to 1 indicates a strong positive correlation, while a value close to -1 indicates a strong negative correlation. A value close to 0 suggests little to no correlation.

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