STA1010 Assignment 1

1. (a) The experimental units in this experiment are the individual batches of drug and the response variable is the percent yield of the drug in each batch.

(b) There are 2 factors, which are temperature and pressure, and 6 treatments.

(c) There are 24 experimental units required for the experiment.

(d) Randomization uses chance to assign subjects to treatments and hence it can be used to prevent bias or systematic favoritism in the experiment. Therefore, some form of randomization should be employed in this experiment such as completely randomized design where all experimental units are allocated at random among all treatments and randomized block design where the random assignment of units to treatments is carried out separately within each block.

2. Boxplot:

n = 21, min = 12.81, max = 36.73

Median = (n + 1)/ 2 = (21 + 1)/ 2 = 11

\Median with rank 11 = 20.88

Q1 has rank (21 + 1)/ 4 or 5.5,

so Q1 = 17.90 + 0.5 (18.27 – 17.90)

= 18.09

Q3 has rank 3(21 +1)/ 4 or 16.5,

so Q3 = 22.16 + 0.5 (22.24 - 22.16)

= 22.2

Hence the IOR = 22.2 – 18.09

= 4.11

The two highest cardiac output values, which are 35.78 and 36.73, are considered to be a possible outlier because they are more than 1.5 x IQR.

3. (a) (i) Stem and leaf plot of the first pulse rates of the female smokers:

6 2

7 6, 8

8 8, 8

9 0, 4

10 0

(ii) Q1 has rank (8+1)/ 4 or 2.25,

so Q1 = 76 + 0.25 (78 – 76)

= 76.5

M has rank (8+1)/ 2 or 4.5,

so M = 88

Q3 has rank 3(9)/ 4 or 6.75,

so Q3 = 90 + 0.75 (94 – 90)

= 93

x = (62 + 76 + 78 + 88 + 88 + 90 + 94 + 100)/ 8

= 676/ 8

= 84.5

s = Ö [(Sxi2 – nx2)/ (n – 1)]

= Ö[(506.25+72.25+42.25+12.25+12.25+30.25+90.25+240.25)/ 7]

= 11.99

(b) (i) Steam and leaf plot of the first rates of the female non-smokers:

5 8

6 0, 1, 2, 2, 4, 6, 6, 8, 8, 8

7 2, 2, 6, 8, 8, 8

8 0, 0, 2, 2, 4, 4, 6, 7

9 6, 6

(ii) Q1 has rank (27+1)/ 4 or 7,

so Q1 = 66

M has rank (27+1)/ 2 or 14,

so M = 76

Q3 has rank 3(28)/ 4 or 21,

so Q3 = 82

(c) From the median, which are 88 for smokers and 76 for non-smokers, we can see that non-smokers have lower pulse rates than smokers on average. Both distributions have similar spread but the distribution is shifted to the right of that non-smokers.