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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