Question

Question 4 options: 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.

Answer 1

The 94% confidence interval is : ( 0.0867 , 0.1933 ) = ( 8.67 , 19.33 )%

Explanation:

Solution:-

- The sample size, n = 150 visitors

- The proportion of visitors who hiked, p = 0.14

- We are to create a 94% confidence interval for the population proportion.

- We will determine the Z-critical value for the CI : 0.94 or significance level α = 0.06

- The critical value is defined and plucked from Z-score (standardized) tables as:

Z-critical = Z_α/2 = Z_0.03 = 1.88

- The confidence interval for the population proportion (p) is constructed as:

`( p - Z-critical\sqrt{(p*(1-p))/(n) } , p + Z-critical\sqrt{(p*(1-p))/(n) } )\\\\( 0.14 - 1.88\sqrt{(0.14*(1-0.14))/(150) } , p + 1.88\sqrt{(0.14*(1-0.14))/(150) } )\\\\( 0.08673 , 0.19326 )`

- The 94% confidence interval is : ( 0.0867 , 0.1933 ) = ( 8.67 , 19.33 )%