Question

1. Given a confidence interval

(0.09, 0.21),

what is the margin of error?

2.

A software engineer is creating a new computer software program. She wants to make sure that the crash rate is extremely low so that users would give high satisfaction ratings. In a sample of 575 users, 23 of them had their computers crash during the 1-week trial period.

(a) What is the sample size?

What is p̂?

(b)

What is the 95% confidence interval for p̂? (Use a table or technology. Round your answers to three decimal places.)

Answer 1

1)

Given upper limit = 0.21

Lower limit = 0.09

Margin of error = (upper limit - lower limit)/2 = 0.06

2)

P^ = 23/575 = 0.04

B)

N = 575

First we need to check the conditions of normality that is if n*p and n*(1-p) both are greater than 5 or not

N*p = 23

N*(1-p) = 552

Both the conditions are met so we can use standard normal z table to estimate the interval

Critical value z from z table for 95% confidence level is 1.96

Margin of error = 1.96*√{p*(1-p)}/√n = 0.01601724288

Confidence interval is given by

P-MOE < P < P+MOE

0.024 < P < 0.056