Question

In: Statistics and Probability

A telephone company claims that less than 20% of its customers have at least two telephone...

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.

Solutions

Expert Solution

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


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