Answer:
t = 4.26
Step-by-step explanation:
Sample, n = 453
Proportion, x = 60%
Required
Test Statistic
Test statistic is calculated as follows
t = (x - p)/(σ/√n)
Where σ = √p(1 - p)
When an experiment is conducted repeatedly, the results moves close to the expected value (Law of large numbers).
Hence p = 0.5
Calculating σ
σ = √p(1 - p)
σ = √0.5(1 - 0.5)
σ = √(0.5 * 0.5)
σ = √0.5²
σ = 0.5
So,
t = (x - p)/(σ/√n) becomes
t = (60% - 0.5)/(0.5/√453)
t = (0.6 - 0.5)/(0.5/√453)
t = (0.1)/(0.5/21.28)
t = 0.1 * 21.28/0.5
t = 2.128/0.5
t = 4.256
t = 4.26 ---- Approximated
