Question

In a random poll of 801 Americans around the country, 57% of them have some form of streaming service. Create and interpret a 90% confidence interval for the percentage of Americans who use a streaming service using PANIC.

Answer 1

Solution :

Given that,

n = 801

Point estimate = sample proportion = =57%=0.57

1 -   = 1- 0.57 =0.43

At 90% confidence level

= 1 - 90%  

= 1 - 0.90 =0.10

/2 = 0.05

Z/2 = Z  0.05 = 1.645 ( Using z table )

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

= 1.645 *((0.57*0.43) / 801)

E = 0.029

A 90% confidence interval for population proportion p is ,

- E < p < + E

0.57-0.029 < p < 0.57+0.029

0.541< p < 0.599