Question

A new rocket launch system is being considered for the deployment of small, short-range rockets. The probability that the existing system will have a successful launch is represented by p = 0.8. A sample of 53 experimental launches is taken with the new system and 42 are successful. Determine the margin of error for a 97% confidence interval for the success rate of the new system.

Use the critical value rounded to 3 decimal places and your answer to 4 decimal places.

Write the answer with 4 decimals.

Answer 1

Solution :

Given that,

Point estimate = sample proportion = $\hat p$ = x / n = 42 / 53 = 0.7925

1 - $\hat p$ = 1 - 0.7925 = 0.2075

Z$\alpha$/2 = Z_0.015 = 2.170

Margin of error = E = Z_{$\alpha$ / 2} * (($\hat p$ * (1 - $\hat p$ ))$\sqrt$ / n)

= 2.170 ($\sqrt$((0.7925 * 0.2075) / 53)

= 0.1209