Question

In a newspaper article, 28% of the 2600 adults polled said the U.S. space program should emphasize scientific exploration.

Calculate a lower confidence bound at the 99% confidence level for the true proportion of adults said the U.S. space program should emphasize scientific exploration. (2 Points)

Regardless of the true value of proportion, how large a sample size is necessary if the error at 96% confidence level is equal to 0.01? (2 Points)

Answer 1

Solution :

Given that,

1) Point estimate = sample proportion = = 0.28

1 - = 1 - 0.28 = 0.72

Z = Z0.01 = 2.326

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

= 2.326 (((0.28 * 0.72) / 2600)

= 0.020

A 95% lower confidence interval for population proportion p is ,

- E   

= 0.28 - 0.020 = 0.260

lower bound = 0.260

b) Given that,

=  1 - = 0.5

margin of error = E = 0.01

Z/2 = Z0.02  = 2.054

sample size = n = (Z / 2 / E )2 * * (1 - )

= (2.054 / 0.01)2 * 0.5 * 0.5

= 10547.29

sample size = n = 10548