Question

A telecommunications company reported that 30% of mobile phone users exceed their data plan allocation. Suppose that you are a data analyst in the company and you want to verify the above claim. You have selected a random sample of 200 customers and you want to determine the likelihood that more than 40% of the customers are exceeding the data allocation of their contract.

Although you are not given a Z-stat table, show with your calculations whether it is likely to observe a proportion of at least 40% of customers exceeding their data allocation. Explain your answer.

Answer 1

here population proportion=     p=	0.300
sample size       =n=	200
std error of proportion=σp=√(p*(1-p)/n)=	0.0324

proportion of at least 40% of customers exceeding their data allocation:

probability =

P(X>0.4)

=

P(Z>3.09)=

1-P(Z<3.09)=

1-0.9990=

0.0010

as probability of  of at least 40% of customers exceeding their data allocation is significantly small,, therefore it is not likely event.