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Q1: The following data shows the liver sizes measured to the nearest 1 cm of 40 chimpanzees. Size…

The following data shows the liver sizes measured to the nearest 1 cm of 40 chimpanzees.

5.0 – 6.0
6.0 – 7.0
7.0 – 8.5
8.5 – 10.0
10.0 – 11.5
11.5 – 12-0
12.0 – 14.0

Calculate the mean, median, mode, standard deviation and quartile deviation.
Prior to a study to investigate a new asthma drug, pulmonary function was tested in a group of 144 individuals with exercise-induced asthma. The mean value of forced vital capacity in the sample was 2.5 litres with sample standard deviation 0.55 litres.
Construct a 95% confidence interval for the mean value of forced vital capacity in individuals with exercise-induced asthma.
Estimate how large a sample would be needed in order to reduce the width of the interval to 0.1 litres.
It is known that the mean value of forced vital capacity amongst the whole population is 2.65 litres. Test at the 1% level whether the data provides significant evidence that sufferers of exercise-induced asthma have reduced forced vital capacity.

Two manufacturers produce two new drugs to help treat severe Hey Fever. Both drugs are known to work well but both seem to produce unpleasant side effects. A clinical trial is conducted to determine which drug is better.

300 Hey Fever patients are treated with drug A and 45 report side effects. Calculate a 95% confidence interval for the proportion of patients suffering side effects from drug A.
Estimate how many more patients would need to be added to the trial in order to reduce the width of the confidence interval to 0.05.
240 Hey Fever patients are treated with drug B and 35 report side effects. Test at the 1% level whether the data suggests that drug B is significantly better than drug A

Experiments carried out over many years show that the probability that a patient has a reaction to Tamiflu is 0.05
A doctor treats 20 patients with Tamiflu.
What is the probability that 2 patient suffers a reaction to the Tamuflu?
What is the probability that more than 5 of the patients suffer a reaction to the tamiflu?
500 patients are treated in hospital with tamiflu.
What are the mean and the variance of the number of patients who suffer a reaction?
Find using a Normal approximation the probability that between 12 and 15 patients suffer a reaction to tamiflu
Among men in Iceland between the ages of 40 and 75, diastolic blood pressure is normally distributed with mean 82mmHg and standard deviation 14.5 mmHg

Calculate the probability that a randomly chosen man has diastolic blood pressure between 84mmHg and 87mmHg.
In a survey a group of 50 randomly chosen men aged between 40 and 80, had their diastolic blood pressure measured. What is the distribution of the mean diastolic blood pressure of the sample?
Find the probability that the mean diastolic blood pressure in a random sample of 50 men aged between 40 and 80, is less than 81.7
How large a sample of women would be required in order that the probability of the sample mean being less than 81.7 is reduced to 0.1?

The snout vent length of newly born snakes is thought to be a reasonable measure of their development. In an experiment the snout vent length of newly born snakes bred in the wild and in captivity were compared. The following data gives the snout vent length (in cm) of 10 newly born snakes bred in captivity.
12, 16, 10, 12, 14, 16, 10, 12, 14, 13

Calculate the sample mean and the sample standard deviation for this data.
Find a 95% confidence interval for the mean length of the snout vent in newly born snakes. You may assume that the snout vent length is approximately normally distributed.
A second sample of snout vent lengths was taken, this time from 20 newly born snakes bred in the wild. The sample mean was found to be 12.2cm and the sample standard deviation was found to be 2.3cm. Carry out a hypothesis test at the 1% level to determine whether there is significant evidence that there is a difference between the mean snout vent length in newly born snakes bred in captivity compared with those bred in the wild.

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