Question

6) An internet service provider sampled 454 customers and finds that 112 of them experienced an interruption in high speed service during the previous month. What is the upper bound 99% confidence interval for the proportion of customers who experienced an interruption. Round to three decimal places.

7) The Nielsen Company surveyed 378 owners of android phones and found that 216 of them planned to get another android. What is the lower bound 95% confidence interval for the proportion of Android users who plan to get another android? Round to three decimal places.

Answer 1

Solution :

Given that,

6)

n = 454

x = 112

Point estimate = sample proportion = = x / n = 112 / 454 = 0.247

1 - = 1 - 0.247 = 0.753

At 99% confidence level the z is ,

= 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

Z_/2 = Z _0.005 = 2.576

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

= 2.576 * (((0.247*0.753) / 454)

= 0.052

A 99% confidence interval for population proportion p is ,

- E < p < + E

0.247 - 0.052 < p < 0.247 + 0.052

0.195 < p < 0.299

Lower bound = 0.195

7)

Given that,

n = 378

x = 216

Point estimate = sample proportion = = x / n = 216 / 378 = 0.571

1 - = 1 - 0.571 = 0.429

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z_/2 = Z _0.025 = 1.96

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

= 1.96 * (((0.571*0.429) / 378)

= 0.050

A 95% confidence interval for population proportion p is ,

- E < p < + E

0.571 - 0.050 < p < 0.571 + 0.050

0.521 < p < 0.621

Lower bound = 0.521