Question

NASA is conducting an experiment to find out the fraction of people who black out at G forces greater than 66.

Step 2 of 2:

Suppose a sample of 566 people is drawn. Of these people, 260 passed out. Using the data, construct the 95% confidence interval for the population proportion of people who black out at G forces greater than 6. Round your answers to three decimal places.

Answer

Lower endpoint:       Upper endpoint:

Answer 1

Solution :

Given that,

Point estimate = sample proportion = = x / n = 260 / 566 = 0.459

1 - = 1 - 0.459 = 0.541

  Z/2 = Z0.025 = 1.96

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

= 1.96 (((0.459 * 0.541) / 566)

= 0.041

A 95% confidence interval for population proportion p is ,

± E

0.459  ± 0.041

Lower endpoint: 0.418

Upper endpoint: 0.500