辅导 STAT7120 Analysis of Scientific Data Semester Two Examinations, 2023调试SPSS

School of Mathematics & Physics

Semester Two Examinations, 2023

STAT7120 Analysis of Scientific Data

Question 1

10 marks

In Lecture 4 this semester both streams chose the following question to answer using Warner’s Method:

If, today, you or your girlfriend would accidentally get pregnant, would you seriously consider the possibility of an abortion?

The instructions given for Warner’s Method were as follows:

□ Toss a coin twice and note the outcomes without anyone else seeing

□ If you had HH then answer the question truthfully

□ If you had anything else then answer the opposite of the truth

Out of all the students who responded to the poll question, 41% said “Yes” .

a) Draw a tree diagram to describe the process described above. Indicate the

probabilities on each branch of the tree, including the unknown probability, #, of interest. [4 marks]

b) Use this process and the observed responses to give an estimate of the true proportion of all students who would answer “Yes” to the original question. [6 marks]

Question 2

14 marks

Suppose X is the number of coffees purchased in a day by a random university student with probability function as given in the following table:

a) What are the expected value and standard deviation of X? [5 marks]

b) Suppose a café aims to service the needs of 100 students, each with the same

probability function as above. What are the expected value and standard deviation of the total number of coffees, Y, they will sell each day? [4 marks]

c) Estimate the probability that the café will sell at least 100 coffees to these 100 students. [5 marks]

Question 3

26 marks

Two colour morphs (green and red) of the same species of sea star were randomly

sampled from a location. The table below shows the radial lengths (mm) of the collected sea stars:

The mean radial length for the 5 red sea stars was 82.8 mm with standard deviation 36.49 mm, while for the 6 green sea stars the mean was 113.5 mm with standard deviation 17.48 mm.

Since the red colour stands out more against the background, the red sea stars may tend to be smaller due to predation. Is there any evidence of this from the data?

a) Define appropriate population parameters and use these to state the null and alternative hypotheses to address this question. [4 marks]

b) Carryout a two-sample t-test to determine whether there is evidence that the mean radial length of red sea stars is less than for green sea stars. [10 marks]

c) State two reasons why your result in (b) might not have given significant evidence at the 5% level. [2 marks]

d) Carryout a Wilcoxon Rank-Sum test to determine whether there is evidence that red sea stars tend to be smaller than green sea stars. Briefly comment on how the result compares to the :-test in (b). [10 marks]

Question 4

24 marks

Biochar is a charcoal that can be added to soil to improve water storage. A study was conducted to investigate the effect of biocharon tomato yield and quality of tomato under three different irrigation regimes: full irrigation (FI), deficit irrigation (DI) and partial root-zone drying irrigation (PRD). Two levels of biochar (0% and 5% by weight) were used with the plants grown in plastic pots in a greenhouse. A total of 42 plants were randomly allocated to each of the six combinations of irrigation regime and biochar level, giving 7 plants in each combination.

At maturity the tomatoes were harvested, and the Vitamin C content was recorded. The researchers also noted whether the pot had attracted insects.

a) The following table summarises the counts of pots that had attracted insects:

Based on this table, is there evidence of an association between insect attraction and irrigation regime? [10 marks]

b) The combined effects of biochar and irrigation on Vitamin C content can be

assessed using Two-way ANOVA. The sums of squares for each component of the ANOVA are shown in the following ANOVA table:

Complete this table by giving the appropriate degrees of freedom and calculating the mean sums of squares, F-statistics, and p-values. [7 marks]

c) What is the R2 value for this model? Briefly interpret the value. [3 marks]

d) Briefly summarise the conclusions you can make about factors affecting Vitamin C content from this analysis. [4 marks]

Question 5

26 marks

Physical activity is beneficial for the improvement of both physical and cognitive functions for older adults and muscle strength is one of the main factors for maintaining physical function in old age. Handgrip strength is considered a good overall indicator for general muscle strength and so a study investigated whether cognitive function is associated with handgrip strength among community-living older adults.

a) The study used a random sample of 38 people and found a mean handgrip strength of 21.2 kg with standard deviation 4.64 kg. Calculate a 95% confidence interval for the mean handgrip strength of all people in this population. [8 marks]

b) The study measured cognition using the Mini-Mental State Examination (MMSE),

giving a score from 0 to 30, where higher values are associated with higher levels of cognition. Suppose the data from this study is loaded in R asa data frame. called grip with variables Handgrip and MMSE. Write down the R expression you would use to obtain the intercept and slope of the least-squares line for the relationship between MMSE and Handgrip. [3 marks]

c) Output from the regression summary in R is shown below:

Coefficients:

Estimate Std . Error

(Intercept) 21.4242 1.4518

Handgrip 0.1971 0.0669

Does this model give any evidence that MMSE is positively associated with handgrip strength? [8 marks]

d) Based on this model, what is the estimated mean MMSE score for older adults with a handgrip strength of 20 kg? [3 marks]

e) The following plot was obtained for the regression model in R:

Briefly explain what this plot is telling you about the model. [4 marks]