Carbon dioxide is known to have a critical effect on microbiological growth. Small amounts of CO2 stimulate growth of some organisms, whereas high concentrations inhibit the growth of most. The latter effect is used commercially when perishable food products are stored. A study is conducted to investigate the effect of CO2 on the growth rate of pseudomonas fragi, a food-spoiling organism. Carbon dioxide is administered at five predetermined different atmospheric pressures. The response measured was the percentage change in cell mass after 1-hour growing time. Ten cultures were used at each atmospheric pressure level, resulting in the following data: 0.0 .083 .29 .50 .86 62.6 50.9 45.5 29.5 24.9 59.6 44.3 41.1 22.8 17.2 64.5 47.5 29.8 19.2 7.8 59.3 49.5 38.3 20.6 10.5 58.6 48.5 40.2 29.2 17.8 64.6 50.4 38.5 24.1 22.1 50.9 35.2 30.2 22.6 22.6 56.2 49.9 27.0 32.7 16.8 52.3 42.6 40.0 24.4 15.9 62.8 41.6 33.9 29.6 8.8
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
1.Carbon dioxide is known to have a critical effect on microbiological growth. Small amounts of CO2 stimulate growth of some organisms,
whereas high concentrations inhibit the growth of most. The latter effect is used commercially when perishable food products are stored. A study is conducted to investigate the effect of CO2 on the growth rate of pseudomonas fragi, a food-spoiling organism. Carbon dioxide is administered at five predetermined different atmospheric pressures. The response measured was the percentage change in cell mass after 1-hour growing time. Ten cultures were used at each atmospheric pressure level, resulting in the following data:
|
0.0 |
.083
|
.29 |
.50 |
.86 |
|
62.6 |
50.9 |
45.5 |
29.5 |
24.9 |
|
59.6 |
44.3 |
41.1 |
22.8 |
17.2 |
|
64.5 |
47.5 |
29.8 |
19.2 |
7.8 |
|
59.3 |
49.5 |
38.3 |
20.6 |
10.5 |
|
58.6 |
48.5 |
40.2 |
29.2 |
17.8 |
|
64.6 |
50.4 |
38.5 |
24.1 |
22.1 |
|
50.9 |
35.2 |
30.2 |
22.6 |
22.6 |
|
56.2 |
49.9 |
27.0 |
32.7 |
16.8 |
|
52.3 |
42.6 |
40.0 |
24.4 |
15.9 |
|
62.8 |
41.6 |
33.9 |
29.6 |
8.8 |
a.State the hypotheses to be tested.
b.Conduct an analysis of variance of the experiment at the 0.05 level of significance, stating any conclusions that could be drawn.
c. Complete the ANOVA table for this test.
d. State the statistical assumptions underlying this test.
e.Write down the classification model for solving the above data.
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