Question

A random sample of 150 visitors traveling in Hawaii found that 14% of them hiked the Legendary Na Pali Coast. Create a 94% confidence interval for the population proportion of visitors hiking the Na Pali Coast. Enter the lower and upper bounds for the interval in the following boxes, respectively. You may answer using decimals rounded to four places or a percentage rounded to two. Make sure to use a percent sign if you answer using a percentage.  

Answer 1

Solution :

Given that,

n = 150

Point estimate = sample proportion = = 0.14

1 - = 1 - 0.14 = 0.86

At 94% confidence level

= 1 - 94%

=1 - 0.94 =0.06

/2 = 0.03

Z/2 = Z0.03  = 1.881

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

= 1.881 (((0.14 * 0.86) / 150)

= 0.0533

A 94% confidence interval for population proportion p is ,

± E   

= 0.14  ± 0.0533

= ( 0.0867, 0.1933 )

= ( 8.67%, 19.33% )