For the following, identify (i) the response and explanatory variable, (ii) the

Question

For the following, identify (i) the response and explanatory variable, (ii) the levels of the explanatory variable, (i) the appropriate degrees of freedom for the ANOVA table (i.e., dfgroup dferror, and dftotal) (iv) the hypotheses of interest. To see how much of a difference time of day made on the speed at which he could download files, a college sophomore performed an experiment. He placed a file on a remote server and then proceeded to download it at three different time periods which he labeled as Early (7am), Evening (5pm), and Late night (12am). He randomly downloaded the file 48 times in all, 16 times at each Time of Day, and recorded the Time in seconds that the download took. A student decides to investigate how effective washing with soap is in eliminating bacteria. To do this she tested four different methods-washing with water only, washing with regular soap, washing with antibacterial soap, and spraying hands with antibacterial spray (containing 65% ethanol as an active ingredient). She suspected that the number of bacteria on her hands before washing might vary considerably from day to day. To help even out the effects of those changes, she generated random numbers to determine the order of the four treatments. Each morning she washed her hands according to the treatment randomly chosen. Then she placed her right hand on a sterile media plate designed to encourage bacteria growth. She incubated each plate for 2 days at 36°C, after which she counted the bacteria colonies. She replicated this procedure 8 times for each of the four treatments A manager wishes to determine whether the mean times required to complete a certain task differ for the three levels of employee training. He randomly selected 10 employees with each of the three levels of training (Beginner, Intermediate and Advanced) to study if there is sufficient evidence to indicate that the mean times required to complete a certain task differ for at least one of the three levels of training? a. b. C.

Explanation / Answer

Solution

a)

i) Response variable: File downloading time

ii) Levels of explanatory variables: 3 levels of time period – Early (7am), Evening (5 pm) and Late night (12 am)

iii) Degrees of Freedom

     Group: (3 - 1) = 2

     Error: 47 – 2 = 45

     Total : (16 x 3) – 1 = 47

b)

i) Response variable: Bacteria count

ii) Levels of explanatory variables: 4 levels of washing – with water only, with soap, with anti-bacterial soap and with anti-bacterial hand-spray

iii) Degrees of Freedom

     Group: 4 – 1 = 3

     Error: 63 – 3 = 60

     Total : (2 x 4 x 8) – 1 = 63

c)

i) Response variable: Time to complete a task

ii) Levels of explanatory variables: 3 levels of employee-training – Beginner, Intermediate and Advanced

iii) Degrees of Freedom

     Group: 3 – 1 = 2

     Error: 29 – 2 = 27

     Total : (10 x 3) – 1 = 29

DONE

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