Homework Answers

Draw a direction plot using given differential equation. Also find the equilibrium

solution and plot.

a) y

′ = −2 + t − y

b) y

′ = 3sint + 1 + y

Consider and solve the initial value problem of a new form of life discovered on a distant

planet. Outside its habitable zone, the rate of change of population of the life form is

governed by the following data:

dy

dx + y = f(x), where f(x) = {

e

−x

, 0 ≤ x < 2

e

x

, x ≥ 2

; y(0) = 1

1. In an obstetric hospital 17.8% of 320 women were delivered by forceps in 1980. What is the standard error of this percentage? In another hospital in the same region 22% of 185 women were delivered by forceps.

(a) What is the standard error of the difference between the percentage at this hospital and the first one? ( 8 marks)

(b) What is the 95% confidence interval of the differences between those two percentages?

(c) Was the difference in proportions statistically significant? ( 3 marks) 

The following are data for 12 individuals’ daily sodium intake and their systolic blood pressure readings. A research investigator is interested in learning how strong the association is between these variables and how well we can predict blood pressure from sodium intake.

Person

1

2

3

4

5

6

7

8

9

10

11

12

Sodium (X)

6.8

7.0

6.9

7.2

7.3

7.0

7.0

7.5

7.3

7.1

6.5

6.4

BP (Y)

154

167

162

175

190

158

166

195

189

186

148

140

a. Calculate the correlation coefficient r and test if it is statistical significant at α = 0.05 level (5 marks) 

b. Calculate the regression equation for data (10 marks)

c. What would be a likely blood pressure for a person with a sodium intake of:

i. 6.3 (2.5 marks)

ii. 7.6 (2.5 marks)

In an obstetric hospital 17.8% of 320 women were delivered by forceps in 1980. What is the standard error of this percentage? In another hospital in the same region 22% of 185 women were delivered by forceps. (a) What is the standard error of the difference between the percentage at this hospital and the first one? ( 8 marks) (b) What is the 95% confidence interval of the differences between those two percentages? (4 marks) (c) Was the difference in proportions statistically significant? ( 3 marks)