Question

An Internet service provider sampled 540 customers and found that 75 of them had experienced an interruption in high-speed service during the previous month. Compute a 99% confidence interval for the proportion of customers who have experienced a service interruption during the previous month.

Answer 1

STEP - BY - STEP EXPLANATION

What to do?

Compute a 99% confidence interval for the proportion of customers who have experienced a service interruption during the previous month.

Given:

X = 75

number of internet service provider ( n ) = 540

Here , X be a customers that experienced an interruption in high speed service during the previous month

X = 75.

And number of internet service provider ( n ) = 540

Proportion of interruption in high-speed provider in previous month is

`\hat{p=(x)/(n)}`
`\begin{gathered} \hat{P}=(75)/(540) \\ \\ =0.1389 \end{gathered}`

Formula of one sample proportion is :

`C.I=\hat{p\pm Z_{\propto|2\frac{}{}}}\sqrt{\frac{\hat{P(1-\hat{P)}}}{n}}`

where;

zα/2= 2.58 (standard normal table value for Z0.005 )

Now;

Substitute the values into the formula.

`C.I=0.1389\pm2.58\sqrt{(0.1389(1-0.1389))/(540)}`
`=0.1389\pm0.03839`

Confidence interval= (0.101, 0.177)

Hence, 99% confidence interval for proportion of customer who have experienced a service interruption during the previous month is ( 0.101 , 0.177)