Question

In a random sample of 300 residents of Arizona, 90 believe that there is intelligent life on Mars.

Find:

a. p̂

b. standard of p̂

c. margin of error for 95% confidence interval for p, the percentage in the population who believe that there is life on Mars.  

d. 95% confidence interval for p

Answer 1

Solution :

Given that,

n = 300

x = 90

a)

Point estimate = sample proportion = = x / n = 0.3

1 - = 0.7

b)

standard error

= (p*(1-p))/n =  (0.3*0.7)/300 = 0.02646

At 95% confidence level the z is ,

Z_/2 = Z _0.025 = 1.96

c)

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

= 1.96 * (((0.3*0.7) /300 )

= 0.052

d)

A 95% confidence interval for population proportion p is ,

- E < p < + E

0.3 - 0.052 < p < 0.3 + 0.052

0.248 < p < 0.352

The 95% confidence interval for the population proportion p is : ( 0.248 , 0.352 )