Question

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 400 users, 20 of them had their computers crash during the 1-week trial period.
Required:
a. What is the sample size?
b What is the 95% confidence Intarval for p?

Answer 1

Answer:

a) the sample size is 400

b) 95% confidence Interval for p is ( 0.0286, 0.0714 )

Step-by-step explanation:

Given the data in the question;

sample size n = 400

x = 20

p = x / n = 20 / 400 = 0.05

q = 1 - p = 1 - 0.05 = 0.95

a)

n = 400

Hence, the sample size is 400

b) 95% confidence Interval for p;

At 95% confidence interval,

significance level ∝ = 1 - 95% = 1 - 0.95 = 0.05

∝/2 = 0.05 / 2 = 0.025

so, Z critical Value ; $Z_{\alpha /2$ = 1.96  { from table }

So for Confidence Interval for p;

⇒ p' ± $Z_{\alpha /2$√( p'q' / n )

we substitute

⇒ 0.05 ± 1.96√( (0.05 × 0.95 ) / 400 )

⇒ 0.05 ± 1.96√( 0.00011875 )

⇒ 0.05 ± 1.96 × 0.010897

⇒ 0.05 ± 0.021358

⇒ ( 0.05 - 0.021358 ), ( 0.05 + 0.021358 )

⇒ ( 0.0286, 0.0714 )

Therefore, 95% confidence Interval for p is ( 0.0286, 0.0714 )