Question

Internet service: An Internet service provider sampled 535 customers, and finds that 64 of them experienced an interruption in high-speed service during the previous month.

(a) Find a point estimate for the population proportion of all customers who experienced an interruption. Round the answer to at least three decimal places.

The point estimate for the population proportion of all customers who experienced an interruption is 0.120

b) Construct an 80% confidence interval for the proportion of all customers who experienced an interruption. Round the answers to at least three decimal places. An 80% confidence interval for the proportion of all customers who experienced an interruption is <p>

Answer 1

Solution:
Given in the question
Number of favourable cases(experienced an interruption in high-speed service during the previous month) X= 64
Number of sample = 535
Solution(a)
Point estimate for the population proportion is same as sample proportion so
The point estimate for the population proportion of all customers who experienced an interruption = X/N = 64/535 = 0.1196 or 0.120
Solution(b)
To calculate 80% confidence interval we will use One proportion Z test so
alpha = 1 - Confidence level = 1-0.8 = 0.2
alpha/2 = 0.2/2 = 0.1
From Z table we found Zalpha/2 = 1.282
80% confidence interval can be calculated as
p +/- Zalpha/2 * sqrt(p*(1-p)/n)
0.120 +/- 1.282 * sqrt(0.120 * (1-0.120)/535)
0.120 + /- 1.282 * 0.014
0.120 +/- 0.018
So 80% confidence interval is 0.102 to 0.138
An 80% confidence interval for the proportion of all customers who experienced an interruption is 0.102 to 0.138