Statistical hypothesis testing - Topic 5

Question 1

Year 2 - Chapter 1

Relationship for the exponential model

(Its equation)

Answer 1

y = kb^x

ꜜ
Y = log(y); X = x

ꜜ
log(y) = log(k) + x(log(b))

ꜜ
Y = log(k) + X(log(b))

Question 2

Year 2 - Chapter 1

Relationship for the geometric model

Answer 2

y = ax^n

ꜜ
Y = log(y); X = logx

ꜜ
log(y) = log(a) + n(log(x))

ꜜ
Y = log(a) + nX

Question 3

Year 2 - Chapter 1

What does PMCC measure?

Full definition

Answer 3

The product moment correlation coefficent describes the linear correlation between two variables. It can take values between -1 and 1.

r = 1, perfect positive linear correlation
r = -1, perfect negative linear correlation
r = 0, no linear correlation

Calculated on the calculator

Question 4

Year 2 - Chapter 1

How to hypothesis test for correlation?

For both one-tailed and two-tailed tests

Answer 4

1. Establish your hypothesis;
   H₀: ρ = 0,
   H₁: ρ > 0 (for positive)
   H₁: ρ < 0 (for negative)
   H₁: ρ ≠ 0 (for two-tailed)
2. Calculate the PMCC of the sample to get r
3. Find the critical value in the correct significance level column from the correlation table in the examboard-issued formula book

(Correlation is symmetrical = for negative correlation, put minus sign in front of number)