2. Doctors are interested in the relationship between the dosage of a medicine and the time required for a patient's recovery. The following table shows, for a sample of 10 patients, dosage levels (in grams) and recovery times (in hours). These patients have similar characteristics except for medicine dosages.

Dosage level	1.2	1.3	1.0	1.4	1.5	1.8	1.2	1.3	1.4	1.3
Recovery time	25	28	40	38	10	9	27	30	16	18

a. Estimate the linear regression of recovery time on dosage level.

b. Find and interpret a 90% confidence interval for the slope of the population regression line.

c. Would the sample regression derived in part a) be useful in predicting recovery time for a patient given 2.0 grams of this drug? Explain your answer.

3. This table is taken from the Financial Times and shows salaries relating to City of London financial positions. The data is based on over 300 posts in almost 150 banks and finance companies. We work for the corporate finance head in one such institution. She (our boss) saw the same table while at a business lunch with a colleague, who holds a position as Eurobond trading head. Over the lunch tempers got a little heated, with each of them claiming that people in their particular job were better paid than those in the other job. The boss has now come back to us and asked for confirmation that she was right in claiming corporate finance heads are better paid than Eurobond trading heads. What can we say?

Using these statistics, and any others you can derive, draft a short management report summarizing the implications of this data.

1. For a random sample of 353 high school teachers, the correlation between annual raises and teaching evaluations was found to be 0.11. Test the null hypothesis that these quantities are uncorrelated in the population against the alternative that the population correlation is positive.