Biostatistics

Biostatistics
In the following, you may use SPSS and web calculators however you like. If you do,
include relevant SPSS output.

Each part except for 1(a) calls for performing a hypothesis test.
Each of the following tests once:
• ?
2 goodness-of-fit test
• z-test for difference of proportions (a.k.a. 2-proportion z-test)
• 1-sample t-test
• ?
2
test for independence and/or homogeneity
1. Recall, from Assignment 2, a researcher exploring students’ attitudes towards group
work, who asked male and female students whether they preferred to work in a group
or to work alone. The following is a summary of the responses collected:
Female Male
Prefers to work alone 22 51
Prefers group work 35 130
(a) For an 85% confidence interval for the difference between the population proportions
of female students who prefer group work and population proportion of
male students who prefer group work,
i. Check if it can be computed: (2 marks)
A. List the assumptions and requirements.
B. State which, if any, are violated, and how you checked them.
ii. Write down the formula you would use to calculate it. (1 mark)
iii. Calculate and report the confidence interval. (1 mark)
iv. Write a sentence interpreting it in the context of the problem. (1 mark)
1
(b) Test if there is sufficient evidence to believe that a greater proportion of female
students prefers group work than that of male students. That is,
i. Define the parameters of interest (if practical) and state the null and the
alternative hypothesis. (2 marks)
ii. Check the assumptions and requirements of the procedure and calculate the
test statistic as follows: (4 marks)
A. List the assumptions and requirements.
B. State which, if any, are violated, and how you checked them.
C. Write down the formula for the test statistic.
D. Report the value of the test statistic and its degrees of freedom, if any.
iii. Calculate the p-value and make a statistical decision at a = 0.1. (1 mark)
iv. State the conclusion in the context of the problem. (1 mark)
(c) Test if there is sufficient evidence to believe that there is a relationship between
attitude towards group work and gender of the student. That is,
i. Define the parameters of interest (if practical) and state the null and the
alternative hypothesis. (2 marks)
ii. Check the assumptions and requirements of the procedure and calculate the
test statistic as follows: (4 marks)
A. List the assumptions and requirements.
B. State which, if any, are violated, and how you checked them.
C. Write down the formula for the test statistic.
D. Report the value of the test statistic and its degrees of freedom, if any.
iii. Calculate the p-value and make a statistical decision at a = 0.1. (1 mark)
iv. State the conclusion in the context of the problem. (1 mark)
2. Recall the data of the locations of certain bacterial colonies on a tissue sample which
has been subdivided into 50 square quadrats of equal area:
2
For your convenience, the counts are reproduced below:
0, 1, 3, 1, 2, 2, 1, 0, 1, 2, 1, 0, 0, 1, 1, 1, 1, 2, 0, 1, 1, 0, 2, 0, 1, 0, 0, 0, 2, 3, 0, 1, 0, 0,
0, 3, 1, 2, 2, 1, 1, 0, 1, 0, 2, 1, 0, 2, 1, 3.
(a) Test that the data are consistent with the counts being distributed Poisson. That
is,
i. Define the parameters of interest (if practical) and state the null and the
alternative hypothesis. (3 marks)
ii. Check the assumptions and requirements of the procedure and calculate the
test statistic as follows: (4 marks)
A. List the assumptions and requirements.
B. State which, if any, are violated, and how you checked them.
C. Write down the formula for the test statistic.
D. Report the value of the test statistic and its degrees of freedom, if any.
iii. Calculate the p-value and make a statistical decision at a = 0.05. (1 mark)
iv. State the conclusion in the context of the problem. (1 mark)
(b) Do the data prove that the population mean is greater than 0.9?
i. Define the parameters of interest (if practical) and state the null and the
alternative hypothesis. (2 marks)
ii. Check the assumptions and requirements of the procedure and calculate the
test statistic as follows: (4 marks)
A. List the assumptions and requirements.
B. State which, if any, are violated, and how you checked them.
C. Write down the formula for the test statistic.
D. Report the value of the test statistic and its degrees of freedom, if any.
iii. Calculate the p-value and make a statistical decision at a = 0.5. (1 mark)
iv. State the conclusion in the context of the problem. (1 mark)
(c) Using the mean and the standard deviation estimated in part (b) (or in Assignment
2), how big a sample would we need to have an 80% chance of detecting
that the population mean is greater than 0.9 using a = 0.05? (3 marks)

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