Question

The acceptable time for answering the phone at a call center is 20 seconds. In a sample of 750 calls, 250 were answered within 20 seconds. With 90% confidence level we can say that the true proportion of calls that are answered within 20 seconds is what?

Answer #1

Solution :

Given that,

Point estimate = sample proportion = = x / n = 250 / 750 = 0.333

1 - = 1 - 0.333 = 0.667

Z_{/2}
= 1.645

Margin of error = E = Z_{
/ 2} *
((
* (1 -
)) / n)

= 1.645 * (((0.333 * 0.667) / 750)

= 0.028

A 90% confidence interval for population proportion p is ,

- E < p < + E

0.333 - 0.028 < p < 0.333 + 0.028

0.305 < p < 0.361

The 90% confidence interval for the population proportion p is :
**0.305 , 0.361**

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