Question

Samuel Morse determined that the percentage of t's being used in the English language in the 1800's was 12%. A random sample of 600 letters from a current newspaper contained 95 t's. Test the claim that the proportion of t's has changed in modern times, using the current newspaper data and a significance level of 0.05. Determine the z score and find the p value ?

Answer 1

H0 : p0 = 0.12

H1 : p0 ≠ 0.12

Sample size, n = 600 ; α = 0.05

Zstatistic < Zcritical ; reject H0

P = 95/600 = 0.16

Zstatistic = (p - p0) ÷ sqrt((p0(1 - p0)) /n)

Zstatistic = (0.16 - 0-12)/ sqrt((0.12(0.88))/600)

Zstatistic = 3.01

Zcritical at 0.05, = - 1.96

Zstatistic > Zcritical