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

Answer:

0.2665

Step-by-step 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.

$\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}$

In which

z is the zscore that has a pvalue of $1 - \frac{\alpha}{2}$.

For this problem, we have that:

$n = 193, \pi = \frac{42}{193} = 0.2176$

90% confidence level

So $\alpha = 0.1$, z is the value of Z that has a pvalue of $1 - \frac{0.1}{2} = 0.95$, so $Z = 1.645$.

The upper boundary of this interval is:

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

So the answer is 0.2665