# Project #3692 - Statistics

In a study of Alzheimer’s disease (a form of dementia) and smoking, the
past smoking habits of patients with Alzheimer’s disease and some
patients with other forms of dementia were determined. In a sample of
29 Alzheimer patients, 15 were smokers. In a sample of 77 patients with
other forms of dementia, 53 were smokers.

(a) (i) In samples of size 29 of patients with Alzheimer’s disease, what
distribution provides a model for the number of patients who
were smokers? Explain the meaning of any symbols that you use.

(ii) In samples of size 77 of patients with other forms of dementia,
what distribution provides a model for the number of patients
who were smokers? Explain the meaning of any symbols that you
use.

(iii) Using the notation that you used in parts (a)(i) and (a)(ii), write
down the null and alternative hypotheses to be used to test
whether the proportion of patients with Alzheimer’s disease who
were smokers is different to the proportion of patients with other
forms of dementia who were smokers.

(b) In this part of the question you are asked to carry out a significance
test for the null and alternative hypotheses that you suggested in
part (a)(iii).

• State the test statistic.
• Write down the null distribution of the test statistic.
• Write down the observed value of the test statistic.
• Report the significance probability for the test.
(ii) State your conclusions from the test.

(a) In a study of food packaging, the number of biscuits that were found
to be broken when a packet was opened was recorded for 75 packets of
biscuits. (Each packet contained 40 biscuits.)
(i) Discuss briefly whether the number of broken biscuits in a packet
should be regarded as continuous or discrete.
(ii) Based only on the context in which the data were obtained,
suggest a model for the number of broken biscuits in a packet of
biscuits, giving reasons for your choice.
(b) Anorexia is a serious illness that can lead to sufferers becoming
dangerously underweight. In a study, the effects of three different
treatment programmes for anorexia were investigated: a standard
treatment programme, a treatment programme involving cognitive
behavioural therapy and a treatment programme involving family
therapy. The weight of each patient was recorded twice, once at the
beginning of treatment and again at the end of treatment.
A statistician analysed the data for the standard treatment group and
the family therapy treatment group. During her analysis, she made
the following notes:

(Worksheet data for this question attatched)
Data source: Professor B. Everitt, Biometrics Unit, Institute
of Psychiatry, London.
Data: Sdiff = Safter - Sbefore and Fdiff = Fafter
- Fbefore, measured in pounds (lb).
Standard treatment: 26 patients, mean −0.45, standard
deviation 7.99, range −12.20 to 15.9.
Family therapy group: 17 patients, mean 3.01, standard
deviation 7.31, range −9.10 to 20.90.
Checked normality using probability plots: OK.
Ratio of variances: 63.82/51.23 ! 1.25.
Mean difference 7.71, with 95% CI (2.88, 12.55).
Two-sample t-test: t = 3.22, df = 41, p = 0.002. Higher
weight gains with family therapy.
Using these notes as a guide, write a brief statistical report of this
statistician’s analysis. Your report should include the following
sections:
• Summary (4 marks)
• Introduction (3 marks)
• Methods (6 marks)
• Results (6 marks)
• Discussion (3 marks)

 Subject Mathematics Due By (Pacific Time) 03/29/2013 12:00 am
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