Question

1.A simple random sample of 800 elements generates a sample proportionp = 0.80. (Round your answers to four decimal places.)(a)Provide a 90% confidence interval for the population proportion._______ to ______

Answer 1

The confidence interval for the population proportion is 0.7767 to 0.82326

Using the confidence Interval Formula :

confidence interval = sample proportion ± z* (standard error)

Mathematically,

• p ± z * √((p * (1-p)) / n)

Zcritical at 90% confidence level = 1.645

Here,

• n = 800
• p = 0.80

standard error = Zcritical × √((0.80 * (1-0.80)) / 800)

Standard Error = 1.645 × 0.01414

Standard Error = 0.02326

Confidence Interval : 0.80 ± 0.02326

• (0.7767, 0.82326)