Quantitative Methods Answers

Using sin( )1.0 = .0 09983 and sin( )2.0 = .0 19867 , find an approximate value of

sin( 15.0 ) by using Lagrange interpolation. Obtain a bound on the truncation error.

A travel agency conducted a survey to find the mode of transport perceived to be the “safest” among their customers. The results showed that 45% of respondents perceive that air planes are the safest. Develop a 95% confidence interval for the proportion of people who think airplane is the safest mode of transportation.

Find a real root of the equation 3x + sinx − e

x = 0 by the method of

bisection, correct to two decimal places.

A curve passing through (0,1),(0.25,0.9412),(0.5,0.8),(0.75,0.64) find the area between the curve x-axis and x=0,x=0.75 by using Simpsons 3/8 th rule

A correlation coefficient is 0.80 and the number of observations is 62.

What is the calculated test statistic? Is this significant correlation

using a 1% level of significance?

A real estate agent wishes to examine the relationship between the

selling price of a home and its size (measured in square feet).

A random sample of 10 houses is selected.

Dependent variable (Y) = house price in $1000s

Independent variable (X) = square feet

House Price in $1000s (Y) Square Feet (X)

245 1400

312 1600

279 1700

308 1875

199 1100

219 1550

405 2350

324 2450

319 1425

255 1700

Last year an average life span of 69 years with standard deviation of

8.9 years was shown by a random sample of 100 recorded deaths in

the Philippines. Using 0.05 level of significance does it seem to show

that the average life span today is greater than 72 years?

Use appropriate Lagrange interpolating polynomials of degrees one, two, and three to approximate

each of the following:

a. f (8.4) if f (8.1) = 16.94410, f (8.3) = 17.56492, f (8.6) = 18.50515, f (8.7) = 18.82091

b. f(-1/3) if f (−0.75) = −0.07181250, f (−0.5) = −0.02475000, f (−0.25) = 0.33493750,

f (0) = 1.10100000

c. f (0.25) if f (0.1) = 0.62049958, f (0.2) = −0.28398668, f (0.3) = 0.00660095, f (0.4) =

0.24842440

d. f (0.9) if f (0.6) = −0.17694460, f (0.7) = 0.01375227, f (0.8) = 0.22363362, f (1.0) =

0.65809197