STA2300 Data Analysis

STA2300 Data Analysis

Question 1

The variable of interest in or studies is the number of survivals of patients. The probabilistic model used to determine the probability is Binomial distribution. The reason for using this model is that the probability of success and failure of an experiment is given.

P (x = 10) = P (x = 10) + P (x = 11) + P (x = 12) + P (x = 13) + P (x = 14) + P (x = 15)

P (x = 10) = 0.206 + 0.219 + 0.17 + 0.092 + 0.031 + 0.005

P (x = 10) = 0.723

Mean = np = 15*0.7 = 10.5

SD = = = 1.484

Mean = np = 45*0.7 = 31.5

SD = = = 3.07

P (x = 40) = P (x = 40) + P (x = 41) + P (x = 42) + P (x = 43) + P (x = 44) + P (x = 45)

P (x = 40) = 0.002 + 0.001 + 0.00003 + 0.00002 + 0.000001

P (x = 40) ~ 0.003

Following are the assumptions:

Each outcome must be classified as a success (the type of outcome that we're interested in) or as a failure. In other words, each outcome must fall into our category of success or not.

Since we're dealing with a count of successes, this probability distribution is discrete.

Each trial is independent. The probability of success (p) and the probability of failure (1-p) is the same for each trial.

Question 2

The variable of interest is “Volume of 330 ml stubby” and the unit of measurement is ml.

P (x < 330) = [330 - 335]/2.4 = -2.083

P (x < 330) = 0.4812

P (332 = x = 342) = [335 - 342]/2.4 - [335 - 332]/2.4 = 0.9982 - 0.8944

P (332 = x = 342) = 0.1038

A randomly selected top 10% bottles been taken out from the sample and were measures by subtracting their volumes with 335 ml. A negative result in the volume means that the bottles are overfilled. Taking the mean of all negative volumes differences would give us with the mean volume of overfilled bottles.

Question 3

The above study was certainly experimental. The reason for such conclusion is that all the conclusions shown in the last paragraph depends on the experiments which were undertaken on almost 1000 respondents.

Carotenoids are the variable of interest for researchers in the study.

A variable that has an important effect and yet is ...