Statistics

STAT100 T3 2015 Assignment 3

Note that [2] marks will be awarded for clear expression and [2] marks for correct use of mathe- matical terminology and notation.

Questions

1 Ebola virus fatality rate

In December 2013 the most widespread epidemic of Ebola virus in history begun in Guinea. It quickly spread in several countries of West Africa and is still ongoing. According to a report of the World Health Organization1 (WHO), as of the end of November 2014 there were 1,327 officially reported deaths out of the 2,164 diagnosed ebola virus cases in Guinea. In epidemiology the term fatality rate refers to the proportion of deaths in the reported cases.

(a) Assuming that the reported data are representative of the population of the whole West Africa region, construct a 95% confidence interval for the fatality rate of the Ebola outbreak. Do this by hand and show all your calculations.

(b) Using the confidence interval in (a) and also the fact that the fatality rate of the Malaria disease can reach (the most severe cases) 20%, justify why the Ebola virus poses a more serious threat than Malaria.

(c) The same WHO report announced 3,145 deaths out of 7,635 cases for Liberia, a neighboring country. Using Rcmdr, report a 95% confidence interval for the difference in fatality rates between these two countries. Include both the input and the output of Rcmdr.

(d) What does the confidence interval in (c) indicate about the rates in the two countries?

(e) Was the assumption of Guinea being a representative sample of the whole West Africa area in (a) valid? Justify your response in terms of the context of the problem.

2 Fertilizers

A researcher wants to test two different brands of fertilizers. Table 1 provides the barley yield from twelve equal plots of land. Each plot was divided in two equal subplots and each subplot was randomly spread with a different fertilizer. We want to test if the difference in the mean yields between the two brands of fertilizers is statistically significant at the 5% significance level.

Plots 1 2 3 4 5 6 7 8 9 10 11 12
Fertilizer A: 56 62 74 94 52 94 97 80 78 44 52 51 
Fertilizer B: 67 72 79 86 71 90 86 65 85 56 61 66

Table 1: Barley yields (kg).

(a) Justify which test is appropriate to use.

(b) Express the null and alternative hypothesis both in words and using mathematical notation.

(c) Using the appropriate test, test if there are significant differences between the mean difference of the two fertilizers’ yields. Include the relevant Rcmdr input and output.

(d) Which fertilizer do you recommend? Justify your response.

3 Protein supplements

Researchers from Victoria University (Cribb et al. 2006) investigated the effects of two different protein supplements in resistance training following a 8-week long study. Their research subjects were 13 recreational male body builders that followed a strict diet. Six were randomly assigned to a whey protein isolate (WI) supplement diet and seven to a casein (C) supplement diet. The WI group had an average gain of 5 kg of lean mass with 0.54 variance and the C group had an average gain of 0.8 kg with 1.12 variance. We want to test if there is any evidence that the supplementation with whey protein leads to greater mass gains and we can assume that both groups come from two different populations.

(a) Formulate the null and the alternative hypothesis using mathematical notation.

(b) Calculate the standard error.

(c) Calculate the appropriate t-statistic.

(d) Using the Figure 1 decide whether there 
is a significant difference in lean mass gains between the two supplements.

**(THERE IS A GRAPH HERE AT THE END OF QUESTION 3. I WILL ATTACH A FILE WITH A PICTURE OF THE GRAPH)**

4 Pitch drop experiment

One of the longest running experiments in science started in 1927 at University of Queensland. The experiment studies the viscosity of pitch and it involves the observation of the flow of pitch through a funnel. The time spent (in years) for each drop to occur is recorded and the measurements of the first seven recorded drops are given below:
8.1 8.2 7.2 8.1 8.3 8.7 9.2.

(a) Given the observations above construct a 95% confidence interval for the average time for a drop to occur. You either do it by hand (show your calculations) and use as your multiplier t∗ = 2.446912or in Rcmdr and include your input and output.

(b) After the seventh drop air conditioning was added which keeps the temperature constant. The next drop occurred after 12.3 years. Using the confidence interval from (a) decide whether the introduction of air conditioning had a significant impact on the experiment.

References
Cribb, P. J., Williams, A. D., Carey, M. F. & Hayes, A. (2006), ‘The effect of whey isolate and resistance training on strength, body composition, and plasma glutamine’, International journal of sport nutrition and exercise metabolism 16(5), 494.

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