In: Statistics and Probability
A telephone company claims that less than 20% of its customers have at least two telephone lines. The company selects a random sample of 500 customers and finds that 88 have two or more telephone lines. Use LaTeX: \alpha α = 0.05 and the P-value method. Correctly state a) your conclusion about what to do with H0 AND b) your conclusion about the claim that is being made.
Answer)
Null hypothesis Ho : P = 0.2
Alternate hypothesis Ha : P < 0.2
First we need to check the conditions of normality that is if n*p and n*(1-p) both are greater than 5 or not
N*p = 100
N*(1-p) = 400
Both the conditions are met so we can use standard normal z table to estimate the P-Value
Test statistics z = (oberved p - claimed p)/standard error
Standard error = √{claimed p*(1-claimed p)/√n
Observed P = 88/500
Claimed P = 0.2
N = 500
After substitution
Z = -1.34
From z table, P(z<-1.34) = 0.0901
P-value = 0.0901
Since the obtained p-value is greater than the given significance 0.05
1)
We fail to reject the Ho
2)
We do not have enough evidence to conclude that less than 20% of its customers have at least two telephone lines