Question

What is the proportion of customers who buy service plans when they buy a computer? To find out, you surveyed 193 customers and found that 42 purchased the service plan. What is the upper boundary of 90% confidence interval for the population proportion? Use Excel and round your answer to two decimal places. Give the answer as a decimal percent (that is, for 10%, give 0.1).

Answer 1

0.2665

Explanation:

In a sample with a number n of people surveyed with a probability of a success of
`\pi`, and a confidence level of
`1-\alpha`, we have the following confidence interval of proportions.

`\pi \pm z\sqrt{(\pi(1-\pi))/(n)}`

In which

z is the zscore that has a pvalue of
`1 - (\alpha)/(2)`.

For this problem, we have that:

`n = 193, \pi = (42)/(193) = 0.2176`

90% confidence level

So
`\alpha = 0.1`, z is the value of Z that has a pvalue of
`1 - (0.1)/(2) = 0.95`, so
`Z = 1.645`.

The upper boundary of this interval is:

`\pi + z\sqrt{(\pi(1-\pi))/(n)} = 0.2176 + 1.645\sqrt{(0.2176*0.7824)/(193)} = 0.2665`

So the answer is 0.2665