The Homogeneity of the Material - Bacteria Growth in Packaged Chicken Drumstick - Statistics Assignment Help

Assignment Task:

Please include your student number in the header of your report.

1. Four different preservatives are being compared to study their effectiveness in retarding bacteria growth in packaged chicken drumsticks. The analysis is done in a laboratory to test the effectiveness of these preservatives over 24 hr periods. Because days could represent a potential source of variability, the experimenter decides to use a randomized block design. Observations on numbers of bacteria are taken for 10 days, and the data are shown here. 

Please pick the four days based on the last four unique digits of your student number. For e.g., if your student id is 09435520, then you model for day 3, day 5, day 2 and day 10. If your student id is, 09435620 then you model for day 5, day 6, day 2 and day 10.

• Analyse four days of data from this experiment (use α = 0.05) and draw conclusions.
• Analyse the residuals from this experiment for the chosen four days.

2. A quarry is studying the characteristics of the stone from a new excavation area. With this aim they are analyzing the statistical distribution of the gravel which passes through the sieve size 2.5 inches. 

Because of the homogeneity of the material, the laboratory has provided a list with the lengths of 50 pieces of gravel as a representative sample of the gravel. Assuming that the sample you have received corresponds with the file sampleN, where N is the last digit of your student number, 

• Provide descriptive statistics for the sample and plot the histogram of the data (Figure 1). Comment on the plot.
• Provide the empirical cumulative distribution function (ecdf) (Figure 2). 
• Based on the histogram and the ecdf, select a suitable statistical distribution. Explain the reasons behind your choice.
• Obtain the parameters of the selected distribution and overlay the corresponding pdf and cdf curves on Figure 1 and Figure 2.
• Calculate empirically the 2.5th and 97.5th percentiles of the sample. Estimate the 2.5th and 97.5th percentiles based on the selected distribution. Comment on the results. 

3. A study was conducted to establish how the heart rate of a cyclist is affected by stress induced by self-reported perceived risks. The study was conducted in two stages:

a. In the first stage, the participants’ heart rates were measured while they were performing cycling maneuvers in a controlled environment isolated from all modes of traffic. The maneuvers were classified according to two factors; course type and difficulty levels. The measured heart rates are presented in Cyclist data. docx (section 1). 

• Plot the data.
• Do the course type and/or the difficulty levels affect the average heart rate?  

b. In the second stage, the participants’ heart rates were measured while they faced different traffic related obstructions in an uncontrolled environment. The participants designated the different obstructions with risk levels and their instantaneous heart rates were measured while they were facing these obstructions. The measured heart rates are presented in Cyclist data. docx (section 2). 

• Plot the data.
• Are the mean heart rates in the two self-reported perceived risk levels different? 
• Discuss whether the variability of the heart rates in the two self-reported perceived risk levels are different or not.

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