HLTH7008: Introduction to Biostatistics - Statistics Assignment Help

Assignment Task

Question 1

Using the Australian CAUCP data set assigned to you and R Commander:

a) Is the measurement of age (variable ‘age’) categorical or continuous? Explain why.

b) Graph the distribution of respondent’s gross annual income (variable ‘income’) with appropriate axis labels.

c) Write one or two sentences describing the distribution of the respondent’s gross annual income (variable ‘income’) using appropriate summary statistics. (Hint: consider measures of centre, spread and shape. R commander output alone is insufficient – write the answer in your own words.

Question 2

Using the Australian CAUCP data set assigned to you and R Commander:

a) Graph respondents’ trust of government scores (variable ‘trust_g’) against their level of satisfaction with the Prime Minister (variable ‘sat_pm’). Using this graph alone, write a sentence or two describing the relationship between these two variables. (Hint: consider centre, spread and shape.)

b) Present the relative frequency distribution of respondent’s level of satisfaction with the actions of the Prime Minister (the variable ‘sat_pm’). Using this relative frequency distribution, write a sentence or two describing respondents’ level of satisfaction with the actions of the Prime Minister.

Question 3

Using the Australian CAUCP data set assigned to you and R Commander:

a) Tabulate the relationship between gender (the variable ‘sex’) and respondent’s level of agreement with using a general lockdown (the variable ‘lockdown’). Include frequency counts and row or column percentages. (Note: R commander output alone is insufficient. Present your table(s) in Word with informative headings.)

b) Using the results in part a) write a sentence or two describing the relationship between respondents’ gender (variable ‘sex’) and their level of agreement with using a general lockdown (variable ‘lockdown’).

c) If you were to select one respondent from this data set at random, what is the probability that they will be a male who agrees with using a general lockdown?d) If you were to randomly select one female from this data set, what is the probability that they agree with using a general lockdown?e) Is respondents’ level of agreement with using a general lockdown (the variable ‘lockdown’) independent of their gender (the variable ‘sex’) in this sample. Support your answer with an appropriate numeric comparison.

Question 4

Using the Australian CAUCP data set assigned to you and R Commander:

a) Suppose you were to randomly select 5 of the 200 respondents in your data set. Explain why the Binomial model may be an appropriate model for the distribution of level of agreement with using a general lockdown (variable ‘lockdown’) for these 5 respondents.

b) Using this Binomial model, estimate the probability that all 5 respondents selected from your data set agree with using a general lockdown (variable ‘lockdown’)? Explain how you derived this answer.

c) Using the Binomial model, in a random sample of 5 respondents, what is the expected mean number of respondents who agree with using a general lockdown? Explain how you derived this answer.

Question 5

Using the Australian CAUCP data set assigned to you and R Commander:

Suppose the distribution of the acceptability of risks to respondents (variable ‘risk’) follows the Normal model.

a) Calculate the mean and standard deviation of acceptability of risks to respondents (variable ‘risk’).

b) Calculate the z-score for a respondent for whom the acceptability of risks is scored at 25. Show your working.

c) Write a sentence or two explaining what the z-score in part b) is measuring.

d) Using the Normal model estimate the proportion of respondents in this sample for whom the acceptability of risks is scored at 25 or more. (1 mark)

e) The Australian CAUCP data set contains 1003 respondents with a mean acceptability score of ????=16.04 and associated standard deviation of ????=5.83. There are 49 students enrolled in HLTH7008 this semester and each has been provided with an independent random sample of 200 respondents the Australian CAUCP data set. Suppose each student calculates the mean of the acceptability of risks score (variable ‘risk’) from their data set. Using the Central Limit Theorem (CLT) describe the expected distribution of these sample means across the 49 students. Explain why the Central Limit Theorem CLT applies.

f) Using the distribution described in part e), estimate the probability that any one student’s sample mean of the acceptability of risks score (variable ‘risk’) has a value less than 15.

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