Quantitative Methods Answers

An experiment to compare the lifespan of four different brands of spark plug was carried out. Five spark plugs of each brand were used, and the number of miles used until failure as an indicator of lifespan was Following is part of the statistical results for a one-way ANOVA.

ANOVA Table

Source of variation

Sum of squares

df

Mean square error

F-value

Treatments

176.5

B

E

G

Error

A

C

F



Total

236.0

D


Find the missing values for A, B, C and D in the ANOVA table.
Perform the ANOVA test to check for significant differences among the population means of the four different brands of spark plugs. Use a 0.05 significance level to conduct the test. The test should include the following steps:
a. State the null hypothesis and alternative hypothesis.
b. Specify the significance level and rejection region.
c. Determine the value of test statistic F. [
d. Determine test decision regarding the null hypothesis.
e. State your conclusion

When you multiply an n digit number by an m digit number manually, then number of digit-wise multiplications you perform is:

scientist why the population of Mathsland continues to grow.]
Year: 1930 1940 1950 1960 1970
Populations: In millions 1.0 1.2 1.6 2.8 5.4
Using a Gregory-Newton method, find the population of the country in 1920?
b) In what year does the expected population reach 60.4 million people?

The equation e^(-Lx)=Lx has a root/zero between x=0 and x=1. This root is approximately at the midpoint of these two x-values. Find this root using a suitable algebra method.
L is 1.55

Evaluate following double integral value taking 4 segment for both x and y direction use Simpson rule ∫(2)_(4)∫(x)_(3x^2) ((3x^2)+y) dy dx

obtain second order derivative y'' using Taylor series Expansion using 4 point

solve the problem d^2T/dx^2 = dT/dt when
T(0,t)=200,T(1,t)=200,T(x,0)=0 using boundary and initial conditions above with dalta x =0.2 solve the parabolic equation for dalta t=0.04 and dalta t=0.015 time step. compare there two results.

A new design of nitrogen charged accumulator, for use in a hydraulic circuit, is being factory tested for certification purposes.(http://www.accumulators.co.uk/). The following data has been collected by a technician:
o Gas volume: V = 0.8 m3
o Gas pressure: p = 160 kPa
o Compression index: n = 1.4
o Pressure/volume relationship: pV ⁿ = C
o Work done =
i. Evaluate C.
ii. Calculate the work done in compressing the nitrogen from 0.8 m3 to 0.6 m3 using:
o integral calculus

A new design of nitrogen charged accumulator, for use in a hydraulic circuit, is being factory tested for certification purposes.(http://www.accumulators.co.uk/). The following data has been collected by a technician:
o Gas volume: V = 0.8 m3
o Gas pressure: p = 160 kPa
o Compression index: n = 1.4
o Pressure/volume relationship: pV ⁿ = C
o Work done =
i. Evaluate C.
ii. Calculate the work done in compressing the nitrogen from 0.8 m3 to 0.6 m3 using
=mid-oridnate rule